The report claims a breakthrough in negotiations has been made, and United now feel the transfer has a strong chance of being completed this summer.
The Barcelona midfielder starred at the recent European under-21 Championships in Israel, and is reportedly available for close to £15m due to a playing time release clause.
Reports this week claimed Thiago has insisted on a similar clause allowing him to leave United if he fails to get adequate first-team football - something ESPN suggest United have agreed.
New United boss David Moyes is thought to be keen to make his first signing a big name, and Thiago would excite the fans as well as filling a position of need for the Premier League champions.
But the club don't have a great record when it comes to long-running transfer sagas.
Wesley Sneijder, Mesut Ozil, Eden Hazard and Karim Benzema have all been heavily linked with United in recent seasons, only before each agreed moves elsewhere.
But there's a feeling within Old Trafford that everything has been done to clinch the signing of Thiago. The Spain under-21 captain has become frustrated with a lack of playing time at the Nou Camp, something United feel they can offer.
With Paul Scholes now retired, Darren Fletcher a long-term absentee and Tom Cleverley and Anderson failing to establish themselves as starting central midfielders, there's space in the squad for a top-level player to slot straight into the starting eleven.