The Millers striker has been out of action for the last three weeks with a quad injury and was set to be missing for another few weeks.
But his recovery has gone better than expected and he will return to full training on Friday, giving him a chance of making Paul Warne’s side at Wembley on Sunday.
Ladapo’s return sees Warne’s options in attack strengthened as Josh Kayode has returned fit from international duty and Michael Smith is fully fit having had an injection to ease a toe injury.
Georgie Kelly, the January signing, is also back in training after a calf injury.
“Smudge is OK, he had an injection in his toe and his heel, which feels a little bit better,” Warne said.
“JJ played only 20 minutes for the (Republic of Ireland) Under-21s last night, so he's good and will be back in the group on Friday.
"Freddie and Georgie have done their last day of rehab and last box-ticking exercise. They passed that with flying colours and they will both be training with us on Friday.
"There's only obviously Griggy (Will Grigg), who is out for the season, so we should have all four available for selection.
"They are a bit match-shy and we normally like to go with two strikers. So I would like to have an option on the bench, at least one.
"I was initially told it would be about six weeks with Freddie, but it's been about three and a half to four with Freddie. It is really good news.
"Georgie had an issue with his calf before we signed him and it just reoccurred and hopefully he comes back a bit stronger before the end of the season to give him game time."
The centre-half is serving a three-match ban in League One after the appeal against his red card in the match with Shrewsbury was dismissed, but he is available for the EFL Trophy showpiece.
Warne added: “Firstly, he’s available for selection in this game, which is good news for us. It was disappointing not to get it overturned, because we felt like we did have a chance.
“I thought it was maybe a little harsh, but then you could also see an argument as to why the referee would give it and they’ve decided to go with his initial decision.”