Manchester United officials will meet with their Barcelona counterparts this weekend in an attempt to thrash out a deal for Pedro, reports ESPN.
The player himself is also expected to be present in the talks with the Red Devils hoping to be in a position to confirm the deal in the middle of next week.
Both clubs are currently touring the USA as part of a pre-season tour and will play each other in a friendly game in San Francisco on Saturday night.
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It is very likely that Pedro will not be involved in the game despite the fact he has been training with the Barcelona squad since they returned from their summer break and is in full health.
The 27-year-old agreed a new contract with his childhood club earlier this year, but has not seen his position in the team change.
With attacking trio Neymar, Leo Messi and Luis Suarez all firm favourites of Luis Enrique, Pedro has found himself playing the role of a back-up player for the best part of two seasons.
Manchester United must agree to pay Pedro's £22m release clause but Louis van Gaal seems more than willing to do so, taking his summer spending above the £100m mark in the process.
Angel di Maria may have to complete his transfer to Paris Saint-Germain before Pedro can be officially signed, but the Argentinian is believed to be closing in on an Old Trafford exit.
The winger has had a torrid time since joining from Real Madrid last season and PSG are rumoured to be ready to pay around £50m to bring him to the Parc des Princes.