The 26-year-old ended the season with 15 goals in 45 appearances for United in all competitions.
After forcing his way back into the team, he was still largely ineffective, and failed to score in his last six games of the season, before being left out against Huddersfield and Cardiff.
Un club insiste pour Sanson — Mercato OM
Pisté par plusieurs clubs anglais, West Ham semble être en pole position. Morgan Sanson a connu une saison délicate avec l'Olympique de Marseille.
New Inter boss Antonio Conte has made the Belgium worldwide his main transfer target this summer, and Lukaku recently labelled the Italian "the best manager in the world" - adding that he "always dreamed" of playing in Serie A.
The source told ESPN that, while Lukaku is not pushing to leave, he feels the time is right for a new challenge and would like to join a club which would make him the centre of their project.
Lukaku, who has been heavily linked with a move to Inter Milan, has a contract at United until 2022.
"I am a big Serie A fan, those close to me know that I have always wanted to play in the English league and in the Italian one, I love Italy".
Suppression de la taxe d'habitation: le calendrier définitif
Cela représenterait, selon les calculs des équipes de Bercy, un gain moyen de 804 euros par foyer et par an dans les deux collectivités réunies.
Belgium's record scorer Lukaku, reportedly valued at £80 million (A$146 million) by United, scored three goals for Martinez's men across two Euro 2020 qualifiers earlier this month.
'It would be a good thing for both parties.
Lukaku did not start a Premier League game under Solskjaer until January, in Solskjaer's seventh game in charge.
MotoGP: Marquez gagne en Catalogne, 1er podium pour Quartararo
C'est l'Italien Andrea Dovizioso (Ducati), le dauphin de Marquez pour 12 points, qui hérite de la sixième place sur la grille. La course reprendra ses droits le 30 juin à Assen, aux Pays-Bas, temple de la vitesse moto.