That's according to Telegraph journalist James Ducker who says the midfielder is currently having a medical.
It's suggested the deal could be announced today or tomorrow - but the latter is more likely.
Ducker said: "Fee was agreed with Chelsea y'day for Matic.
"Having medical today. Announcement today or tomo. More likely tomo at this stage #mufc"
Matic was left in London and didn't travel with the Chelsea squad for their pre-season tour of Asia earlier this month.
Jose Mourinho is desperate to land a holding midfielder with Champions League football returning to Old Trafford next season.
The Portuguese chief worked with Matic during his time in the hot seat at Stamford Bridge.
Starsport understands he's a huge admirer of the Serbia international and has been desperate to secure a reunion with the 28-year-old.
United have been also linked with versatile Tottenham midfielder Eric Dier.
However, having sold Kyle Walker to Manchester City, Spurs are determined not to lose another first-team star.
United have already snapped up Romelu Lukaku from Everton and Victor Lindelof from Benfica in recent weeks.
