West Ham United will take on Manchester United or Shrewsbury Town in the next round of the FA Cup.
The Hammers progressed to the quarter-finals of the competition by beating Blackburn Rovers 5-1 on Sunday afternoon.
And Wilkins now makes West Ham the second favourites to win the competition behind Chelsea.
“Apart from Chelsea, I think West Ham can win it,” Wilkins said. “I think Slaven is going about it in completely the right fashion. Away from home they have beaten everybody it at the top.
“In Payet they have a match winner on their hands. He does the ugly stuff as well. I think they have a really good chance, this is a good West Ham team we’re watching.”
Manager Slaven Bilic has already gone on record to state that he would rather win the FA Cup than quality for the Champions League this season, and his line-up for the Hammers' weekend tie proved how seriously he is taking the cup competition.
West Ham took on Blackburn in the fifth round and they showed no signs of complacency against their Championship opponents.
Although the Hammers did fall behind in the contest early on, they proved their quality as the match progressed.
Victor Moses put West Ham back on level terms, before Dimitri Payet scored a free kick to put the London side into the lead.
After that, Bilic’s men never looked back and they scored twice through Emmanuel Emenike, before Payet wrapped the victory up in the last minute.
West Ham will now play the winner of Manchester United’s tie against Shrewsbury Town in the quarter-finals in March.