There are strong rumours of Pogba's relationship with United boss Jose Mourinho breaking down beyond retrieval at the root of this transfer talk.
Bartomeu could also include the likes of Yerry Mina or Andre Gomes to sweeten the deal for Mourinho.
Having won the World Cup this summer, Pogba is said to have become increasingly frustrated with Mourinho's attempts to play down the achievement.
Pogba's agent, Mino Raiola, now appears to be touting the midfielder to other clubs.
Even after the signing of Brazilian Malcolm and Chile's Arturo Vidal, Barcelona signaled they would continue to seek reinforcements in the market, and this time it is Frenchman Paul Pogba, now at Manchester United. The Hornets have bid £10m for the 23-year-old.
United begin their league campaign on Friday evening against Leicester City.
Striker Romelu Lukaku showed his all-round quality in Belgium's run to third place at the finals and proved he can offer more than being just a battering ram target.
"It's down to the manager to get the best out of him, setting the team up and setting Pogba up in the right way to achieve the best", said the former England central defender.
The World Cup winning midfielder returned to United in 2016 following a spell in Italy with Juventus.
However, late arrivals remain a possibility, especially after Calum Chambers was allowed to leave for Fulham on a season-long loan yesterday.
Despite the fact that United's "not for sale" stance has been widely reported, it hasn't been enough to completely kill off speculation that Pogba might still be on his way.