Jenas has backed Leicester City to win the league title this campaign, Tottenham to finish second and Arsenal to end up third.
The former Newcastle United star believes that West Ham will finish above Manchester City and Manchester United in fourth spot.
"Form and momentum will make all the difference in terms of who finishes fourth,” Nevin told BBC Sport. "West Ham are in great form right now, Manchester City aren't - and Manchester United are just too up and down.
"Looking at those three teams, player for player, if the Hammers can keep everyone fit they can sneak in there, although things are so close it is just a toss-up really.”
City are fourth in the Premier League table at the moment, but West Ham in fifth can certainly pip them to the final Champions League spot.
The London outfit are in better form than City and United, and they will surely fancy their chances of a top-four finish this campaign.
With star player Dimitri Payet in red-hot form at the moment, Slaven Bilic’s side can certainly clinch a Champions League spot.
City and United, though, will make it hard for them, especially as the Citizens have arguably the best squad in the Premier League.