Jose Mourinho has had the 20-year-old goalkeeper on trial in recent weeks as he looks to recruit a new goalkeeper.
The Portuguese boss already acquired Lee Grant on a free transfer in the summer to provide competition for David de Gea and Sergio Romero.
But Woolston will be competing for a spot in the Under-23 squad with Matej Kovar and 18-year-old Alex Fojticek.
The Manchester Evening News claim United coaches were keen to conclude a deal for Woolston last month.
But despite the delay in getting a contract signed, Woolston is expected to put pen to paper on a deal today with the club set to confirm the news imminently.
Woolston previously spent time at Darlington and Sunderland’s academies before a spell in Newcastle’s youth ranks.
However, Woolston was released by the Magpies but he now looks set for a second chance with the Red Devils.
The club have sent Dean Henderson, Joel Pereira and Kieran O’Hara on season-long loans and have now been left short in the goalkeeper department.
Elsewhere, recent reports suggest Mourinho is worried his No 1 David de Gea could leave the club on a free transfer to Juventus.
The 27-year-old is out of contract next summer and the club have the option to extend for a further year.
But The Times say Juventus are willing to play a waiting game to get their man – just as they have done in the past.
A Manchester United insider told The Times said: “De Gea played against his future club on Tuesday. Juve are an expert in intelligent deals.
“If United don’t sell him in the summer, Juventus will wait until the end of his contract.”
De Gea has often been linked with a move to Real Madrid in the past but it seems the Serie A giants are now in pole position to try and lure him away from Old Trafford.
The Spain international failed to keep a clean sheet against Juve in midweek as Massimiliano Allegri’s side recorded a 1-0 win in the Champions League.