Not as far as I know. One of the problems would be that the pair is not at a fixed distance, so you would have to integrate over the possible relative positions. This can give some spectral effects (see attached), but would not give you the information you would like to get. 

I agree with the statement above but would like to build on it a little more.

It is true that you would not get a constant fixed distance between your donor and your acceptor and this could lead to a broad distribution of energy transfer rates (centered around the rate that is determined by the average distance between the donor and acceptor).  If you are working in a dilute solution it is possible that the average distance between donor and acceptor is too large and that there is no energy transfer.  

So in short, yes you could have FRET energy transfer in solution but it would be sensitive to concentration.   Also, remember that working in high concentrations could lead to other problems (internal filter, self quenching.... etc)

Maybe I should remove a possible misunderstanding: I do believe FRET occurs in solution, and it probably does contribute to concentration quenching as Adam suggests (an issue we explore in the paper I attached), although as far as I know this is still under debate. I don't think, however, also in view of the other problems Adam mentions, that it is a useful technique in solution. Having said that, I looked in the literature, and found the attached paper. This answers Irfan Ahmad's question, since they give a donor-acceptor pair that shows FRET in aqueous solution: Fluorescein and Rhodamine 6G, and even give a possible application.

Thank you Adam and Gert Van der Zwan for explaining it. It helped me alot.  The attached articles are useful.

Thanks again.

Much of the FRET work is actually done in solution. However, you correctly assume that much of the recent precision work has been done by conjugating fluorophores to proteins, DNA, quantum dots, etc. See e.g. the works of Medintz, Tinnefeld, Seidel, Flemming, Scholes, etc. This is because the dyes have to be close together and preferably have a relatively narrow distribution of separation distances.

On the other hand, there are ways to examine FRET, if that's your goal, in solution without conjugating dyes to other structures. Much of that work involves confining the dyes in micelles, see e.g. the work of Bhattacharyya. 

So I was working with my molecule. it excites in UV region.  FRET couldnt  work in UV region using an acceptor , it results in quenching/shielding.  I think it is because the acceptor excited along with the donor in the UV region. I think I might need to change the sensing method.  It is really wired for me. Any idea or suggestion. Thanks

Ifran, your comment above is a bit muddled. So I'll try to be helpful with general tips:

1-You need overlap between the donor states and acceptor states for FRET to happen. This is typically achieved by picking molecules so that you have overlap between the donor emission and acceptor absorption spectra. So that's the first thing to check.

2-In order to measure FRET, it's best to reduce forms of cross-talk. So pick an excitation wavelength that is absorbed only (or primarily) by the donor and not at all (or very little) by the acceptor. Hopefully you have also chosen your molecules so that this is possible: i.e. too much overlap of the absorption spectra can make measurements difficult. I

f measuring steady-state fluorescence, remember to subtract the spectrum associated with "direct excitation" of the acceptor prior to calculating FRET efficiencies from "acceptor sensitization".

If measuring time-resolved fluorescence (or using pump-probe spectroscopy) at a single wavelength, make sure you've chosen a wavelength with primary emission from your acceptor (for acceptor sensitization) or primarily emission from your donor (for donor quenching). If this type of cross-talk (e.g. overlap of donor and acceptor emission) is unavoidable, you need to account for it when modeling your data. Similarly, you should account for direct excitation of the acceptor. Both of these will cause departures from single-exponential FRET dynamics by contaminating the detected signals with other components.

3-Not sure what you mean by quenching. Quenching can occur for many reasons. Donors can be quenched via FRET interactions. But I'm guess you mean that the acceptor was quenched. This can occur when dyes are too close to one another; they can form dimers and begin acting like molecular excitons. For example,  J-aggregates typically have reduced emission. One way to check for these interactions is to look for changes in the absorption spectrum when the two dyes are present: for example, significant broadening or an additional peak not present in the constituents. The coupling that leads to dimerization typically requires overlapping states, just like FRET. However, the closer the absorption spectra of the two dyes, the larger the splitting associated with dimerization and therefore the more noticeable these spectral changes will be. If this is the case, try to make your dyes further apart or change your acceptor dye to something at a longer wavelength.

Hope that was helpful.

Actually, the donor excited around 250 nm , which falls in UV range . And the acceptor excitation spectra overlap ( not much) the emission spectra of donor and apparently makes the pair good for FRET. But the acceptor has a small peak near 250 nm ( it might be due to benzene ring) , which is the trouble here. I am trying to find other fluorescence techniques.