Ramsey has also met David Moyes at Everton and Arsene Wenger at Arsenal and must now choose the club he wants to move to.
With Everton and Arsenal there is no loan back agreement but both teams would look to utilise Ramsey ASAP in the first team squad.
All three clubs have match the valuation set by City of around £5m.
"I spoke to Aaron on Friday night," said Peter Ridsdale
"He told me he'd had a great day at United and was on his way to see Arsene. After that, the final decision is up to the youngster himself.
"Aaron spoke to Sir Alex Ferguson before visiting United. He's a sensible person and will listen to what Arsene has to say."