You left out Newcastle United, who has two outstanding matches and is only six points behind Manchester United; if they win their two outstanding matches, they will have a chance to qualify for the Champions League ahead of Tottenham and Liverpool.
Newcastle United are a good team but I do not know if they are good enough to compete wtih Tottenham and Liverpool. I know they have games in hand and are behind Manchester United but they have the worst players and they have been playing worse then they were in the 1st half but I know what you are saying and I agree they could be a threat to the top 4 but I still think it will be out of Newcastle United, Tottenham and Liverpool for the 4th position. I think Manchester United are safe and Manchester City. Arsenal is going to win by a lot of points in my opinion.
Eddie Howe done good job in early part of this season and there were hopes about them to be stayed into top five spots, but their last 10 matches give them big below, and now they are fighting hard for staying into top fives spots which is looking not good because their performance is at the decline, and they are losing points consistently right now they are at fifth and have two matches in hand which can give them better spot above Tottenham if they are able to win, but their schedule is not easy as now they have few tough matches in coming weeks.
With Arsenal and Manchester City are having top ranks and Manchester United is good for the third spot but now for the remaining six spots we have three teams which will be fight and here Tottenham is surely favourite for the fourth, but any prediction is not easy while Liverpool is also going to challenge them, but things could be interested in last few matches.