The Belgian striker is still nursing an ankle problem and faces a race against time to prove his fitness ahead of a meeting with Chelsea at Wembley Stadium on Saturday.
Jose Mourinho has already conceded that the 25-year-old may only be ready for bench duty after sitting out three games at the end of the Premier League season.
Cole, though, believes that the Red Devils should be willing to take a risk on their 27-goal top scorer after seeing him star during a productive debut campaign at Old Trafford.
The former United striker told the club’s official website: “I've watched him all season, like everybody else.
“I think he looks fantastic. To get the goals he's got this season, in a team that doesn't create loads of chances for him, he's done brilliantly and really well considering it's his first season at Old Trafford.
“It's not nice when you've got that little bit of rhythm and pick up an injury. You know you've got a massive game coming up and are a bit touch and go or whatever. So it may be difficult for him but, hopefully, he'll be passed fit and do the best he can.
“It's not every year you're going to get to the FA Cup final. There are no doubts that, if he's even 90, 80 or 70 per cent fit, he'll give it a go.”
Lukaku picked up a knock during a 2-1 victory over Arsenal on April 29, with that issue forcing him from the field five minutes into the second half.
He has not figured for the Red Devils since, but will be desperate to play some part in the pursuit of major silverware against his former employers at Stamford Bridge.