Carroll has already spoken about his delight at moving from Wigan Athletic to the Premiership champions but sources in Lisbon claim United made two further bids for Benfica star Enke on Tuesday.
"Roy will have his medical tomorrow and, all being well, should be unveiled on Friday," agent Francis Martin told planetfootball.com.
"He has agreed personal terms and is looking forward to the challenge of playing for United.
"He has learnt his apprenticeship at Wigan and is ready to make the step up."
Earlier, Enke's name was again being linked with a move to United, following alleged contact in Nyon, Switzerland.
Benfica officials Manuel Vilarinho, Filipe Luis Vieira and Antonio Simoes are believed to have considered two fresh bids for German keeper Enke, finally deciding against selling the player, even though he only has one year left on his contract.
The Portuguese giants would prefer to tie the 24-year-old to a new contract and have deemed one possible replacement, Quim, too expensive.
Enke has already rejected overtures from Ferguson and insisted he will remain at Estadio da Luz for at least another season.
However, it looks as though Carroll is clearly the top target as he spoke about his £2.5 million transfer for the first time.
"It will be great working with Fabien Barthez because, at the moment, there is no better goalkeeper in the world," said the Northern Ireland international.
"The whole deal has not sunk in yet. I will be working with Fabien Barthez and facing shots from David Beckham in training - it's incredible.
"I'm over the moon and I just hope everything will be sorted out."
"I've had a few disappointments before so I'm just keeping my fingers crossed that everything goes through okay.
"I thought I was going to Leicester, then Everton came in for me, but both deals fell through."
