I don't think they wait for Champions League draws or fixtures and neither does CL care much for the PL ... all other leagues allow the teams in Europe to change their fixtures even on short notices to give them time around their ties but no we don't do that because we are special you know ... I am very worried for that "fixed" Carabao Cup Final where a CL semi final first leg could very well be put 48 hours later on the Tuesday. Remember Pellegrini's tenure we had to almost forfeit a cup tie against Chelsea because of same situation where CL won't budge from Tuesday and asked to change domestic tie and domestically we all know we just don't change anything if it's fixed and that time too it was on Sunday where BBC wanted us and won't move to Saturday ...
To answer your question, and looking at how they have announced so far this season, my guess is that we will find out about the first two gameweeks of May at some point in this coming week, could be as early as Monday ... so our tie against Palace away and Chelsea at home would find a TV slot ... and the last game is fixed as well and since all will be on TV, they'll not need to wait till the second last game is played to announce TV picks for that last weekend either.
It's the two gameweeks in between those (Newcastle away and Brighton away for us) is what will probably not be announced till maybe even start of May. They haven't yet decided if that Newcastle mid-week of 11/12 May is being moved to mid-week of 18/19 May and accordingly the teams in FA Cup Final (and who they are supposed to play against on 15/16 May) would have their PL games moved to the one mid-week that is free in the end (as it stands that is 18/19 May, but could very well be 11/12th one).