It is not possible in the same solution. However shifting is possible once you make a mixture oif this solution with a solution which has absorption band coinciding with the fluorescence of first (your solution). Even without fluoresence also it can work with low efficiency. Another method may be that you adsorb a thin layer of your solution on gold nano island having thin film. In this case peak shifting will be observed due to plasmonic effect.
Actually, in principle you can redshift the absorption maximum by using solvents with higher refractive index/stronger dispersion on the condition that there are no chemical changes of your solute. This is known as Kundt's rule, see e.g. Article The Bouguer‐Beer‐Lambert Law: Shining Light on the Obscure