I don't think they need a winger, unless Sterling forces a move. Rodgers clearly rates Ibe and along with Lallana, Sterling, Markovic and Coutinho all being able to play that position I think they're covered.
It really depends what their vision is for next season. If they want to "just" improve on this season I think they need a top draw striker, a top level midfielder (DM ideally), a solid right back and a quality goalkeeper. That's four first team player's who would instantly replace the likes of Mignolet, Johnson, Lucas/Allen & Gerrard in their starting line-up. However I don't think that will get them into the top 4, as I believe the current top 4 will all strengthen hugely and United are very unlikely to have such a poor start.
If I were a Liverpool fan I'd be looking at more than that, I'd be looking at a proper clear out. I wouldn't be bothered if Johnson, Mignolet, Lovren, Toure, Gerrard, Lambert, Balotelli, Borini, Enrique, Lucas and possibly Allen were all let go and were replaced with 7 solid player's who'd contribute far more (goalkeeper, 2 central midfielders, 2 central defenders, a right back and a striker, with Origi also coming into the fold)
The last thing we need is a major clear-out again. However if that is mainly of squad players rather than first teamers then I would be happy with that. As far as the first team is concerned then, after we switched to 3 at the back, we have shown very good form when we have had a relatively injury-free squad to choose from.
Arrivederci (10 - 11 players including 4-5 currently away on loan): Gerrard, Johnson (good as a backup but Flanno should be back and Jonno is on high wages), Jones, Coates (loan - never coming back), Aspas (loan - never coming back), Lambert, Borini, Alberto (loan - never coming back), Toure (i'd keep him as 4th choice but I guess he'll go), Wisdom (loan - doubt he'll ever be good enough, not exactly getting rave reviews now, just solid). Teixeira (currently on loan, and doing very well, at Brighton) will be going on the Summer Tour, I hope he proves himself as he is another player I really like, otherwise I guess he'll be sold too.
Lucas I'd keep as backup (he may not agree though and prefer a move to Italy for regular football). We missed him during this recent period of injury.
BR is never going to let Allen go. I feel we are too light-weight in CM but a strong replacement for Lucas should change that.
GK - Ming has been one of the best keepers in the PL since returning after being dropped. I'd like another keeper to challenge him, Cech would be perfect.
Lovren won't want to go (new contract, nice salary) so it will be difficult / impossible to move him on so I guess we are stuck with him. Fine, so long as he is 4th/5th choice. I'd like to see Ilori brought back and given a chance, he's tall and has fantastic pace for a CB. So if Ilori comes back and Toure goes then we won't be going for another CB, if Ilori doesn't come back then we will of course.
Strikers : I'm also concerned at the lack of headed goals in the team*, we surely have the smallest front 6 in the PL when Sturridge is out, not that he's fantastic in the air either ; Sterling, Ibe, Lallana, Allen, Coutinho, Henderson (who's easily the tallest). We need another very good striker to partner Sturridge.
Origi is very young and has zero experience of the PL, I expect him to need at least 1-2 seasons of irregular starts. So two more strikers or one and keep Balo (as 4th striker he is fine by me) would give us : Sturridge, A.N.Other, Origi and either Balotelli or Ings (?).
So for me this Summers transfers are not going to be too much, probably : one GK, one CB (only if Ilori doesn't come back and is sold), one DM (start ahead of Lucas or to replace him, with Can as backup, if he goes), one CM (replace Gerrard), 2 strikers (or one if Balo stays as #4). If that's the case then even if the budget is as low as £35-40m (I don't think FSG have never made less than that available) plus sales should just about cover it, though I'd expect more with the substantial increase in PL money next season.
*Most Headed Goals 2014/15 (as of 22nd Feb.) : 15 - West Ham, 9 - Stoke, Arsenal, WBA, 8 - Hull, 7 - Man Utd. I have no idea how many Liverpool have but I'm guessing no more than 2-3 at most !