If you can, add some deoxidizer. For example, aluminium or zirconium. 

If you can't, you need to melt under vacuum or controlled atmosphere.

Thanks Fernando. Deoxidizer is an option, but it means reaction and slag formation. Slag needs to be removed. Protecting atmosphere is helping a lot and it's mostly the weapon of choice.

Is there any element such as Gold or Platinum, which stays in the melt, but decreases the oxygen solubility?

In principle, Au and Pt, as well as Pd and other platinoid metals, should decrease oxygen solubility in liquid silver, as all these elements are more noble than silver (Delta G of formation of the oxides higher than for silver oxide). In the PhD thesis of Claude Lupis (1965) he indicates positive interaction coefficients for those metals, what means lower solubility.

If you need oxygen determinations in solid metals, our lab can do that.

Great Fernando, exactly what I was looking for. Thanks a lot!

You may find worthy to check another thread which discusses the possible interdependent effect of other gases at the solubility of a particular gas in a melt:

https://www.researchgate.net/post/If_the_pressure_of_a_gas_is_the_only_factor_that_determines_the_amount_of_dissolution_of_it_in_melt_why_the_other_gases_dont_affect_it