West Ham are currently in sixth place in the Premier League table, but they are closing in on the Champions League chasers.
The Hammers are currently five points behind Manchester City, who occupy fourth place, and they have a game in hand.
With City having the added distraction of still being in the Champions League, at the semi-final stage, and still having to play against Arsenal, their place in the top four is far from secure.
West Ham are still the outsiders in the race, with Manchester United also ahead of them, but Sidwell believes that the London club could come out on top.
“It wouldn’t surprise me if West Ham creep in there, the way this season has gone,” the Brighton midfielder said. “That would top this season off. They deserve some kind of European football, which they’ll get.”
Green, who used to play for West Ham, was more conservative about his prediction for his former side.
The Queens Park Rangers stopper feels that the Hammers may come up just short this season, although he hopes they prove him wrong.
“For me, I’d love them to do it. It’d be fantastic for them to beat Manchester United in the last game at Upton Park and go to the Olympic Stadium with Champions League football,” Green said.
“It’s probably a step too far. They have to win every game and hope things go their way. It’s just a bit beyond them - it’ll probably stay how it is.”
West Ham’s remaining fixtures this season come against Swansea City, Manchester United and Stoke City.