Gary Neville has predicted who will qualify for next season's Champions League, with Chelsea among the five clubs chasing just three spots. Newcastle United, Manchester City, Nottingham Forest, and Aston Villa are all looking to secure their qualification in Europe's biggest club competition.With Liverpool and Arsenal guaranteed places, the Premier League's final weekend will be action-packed. Only three teams will get into the three coveted places, and Gary Neville does not think that the Blues will make it. The Manchester United legend explained on Sky Sports (via Metro):"That was a really important win for Nottingham Forest. They’re still up against it a little bit and they’ve got a big game coming up next weekend. Obviously Man City still have two games but they’re two difficult games actually."Bournemouth are a tasty opposition and then they’ve got Fulham on the final day. City will be flat after losing the cup final. They need to get themselves back up for those games and finish the job off. ‘There’s a lot to play for in the next week and a lot of money at stake."Neville finished:"At the moment I think Man City will just get in there, I think Newcastle will get in there and I think Aston Villa might just sneak in. I think Forest might just hamper Chelsea next weekend and Aston Villa should win at Old Trafford, everyone is beating Man United at the minute."The clubs are incredibly close at the moment: Newcastle, Chelsea, and Villa are all 66 points, while Manchester City and Nottingham Forest both have 65 points. City do have a game in hand, however, as they face Bournemouth on May 20 before their season-ending match away to Fulham.On the final day, Newcastle will host Everton in a bid to consolidate their grip on the third position. Aston Villa will travel to Manchester United at Old Trafford to beat them and gain a Champions League charge. Meanwhile, Chelsea will travel to European hopefuls Nottingham Forest.Chelsea beat Manchester United 1-0 in penultimate Premier League matchChelsea beat Manchester United 1-0 at Stamford Bridge on May 16 as Marc Cucurella's 71st-minute goal gave them the victory. The Blues' victory saw them rise to fourth in the Premier League standings, where they maintained their Champions League hopes ahead of the final matchweek.The match was a tight one, with both teams creating opportunities. Blues' captain Reece James struck the post shortly after the start of the first half. Meanwhile, United's Harry Maguire saw his effort ruled offside.The Blues eventually opened the scoring when James delivered a perfect cross that Cucurella headed home. Meanwhile, Manchester United's loss was their 18th league loss of the season, a new record for the club. They are still 16th in the standings, two positions clear of the relegation zone.