The Red Devils have so far failed to offload the out-of-favour full-back this summer.
Darmian is surplus to requirements at Old Trafford and has fallen even further down the pecking order since Aaron Wan-Bissaka’s arrival for £50m.
The 29-year-old defender has made just 60 Premier League appearances for United as he enters his fifth season with the club.
Solskjaer is ready to flog the defender, however, he faces losing Darmian on a free transfer at the end of the campaign.
The 2015 signing from Torino is poised to return to his homeland of Italy in the summer of 2020.
And his destination will be the San Siro as he teams up with Lukaku again at Inter, according to Rai Sport.
Manchester United sold the striker to Antonio Conte’s side on deadline day last Thursday.
Lukaku left in a deal worth £72m, meaning the Red Devils made a small loss on their top goalscorer last season.
“Inter will be able to formally negotiate terms over a pre-contract from January”
Lukaku only joined United two years ago from Everton for £75m but he has already been and gone in the time Darmian has been at the club.
Now, though, the defender’s future looks set in stone after another summer of speculation surrounding a potential return to Italy.
It appears Darmian will see out the season at Old Trafford as a back-up within Solskjaer’s squad before signing for Inter when his contract expires.
Inter will be able to formally negotiate terms over a pre-contract from January.
And with Darmian having reportedly given his approval to the move, it should prove far more straightforward than the Lukaku saga both clubs endured this summer.
While Juventus, like with Lukaku, have been linked with Darmian, Inter have stolen a march on their rivals.
Barcelona was also touted as a shock destination earlier in the window as a back-up option at the Nou Camp, but no switch materialised.
It means Darmian is likely to face a quiet final campaign with United, as Solskjaer has preferred options at right-back and left-back.
Wan-Bissaka and Luke Shaw are his first choices for the two roles, while club captain Ashley Young, Marcos Rojo, Diogo Dalot and even Axel Tuanzebe are all felt to be ahead of Darmian in the pecking order.