Lukaku only returned to Stamford Bridge in the summer of 2021 on a £97.5m deal from Inter, but has endured a rough time back in west London.
The Belgium international ended the season with just eight Premier League goals in 26 games, falling behind Kai Havertz in the pecking order. He was also scrutinised for giving an interview with Italian media midway through the campaign in which he declared his intention to return to Inter one day.
Chelsea would not stand in Lukaku's way should a suitable offer from Inter arrive this summer, but it is now understood that other European heavyweights are keeping tabs on his situation too.
Spanish giants Barcelona and German champions Bayern are actively being informed of his future. Chelsea would rather sell but are open to a loan in which most of his wages are covered.
However, Lukaku's preference would be to return to Inter, where he helped end their 11-year wait for a Serie A title.
He scored 64 goals in 95 games for the Nerazzurri, forming a prolific partnership with Argentine forward Lautaro Martinez. Should he complete a return to San Siro, Inter hope to pair him with Paulo Dybala following the expiration of his Juventus contract.
Lukaku was asked about his future recently while on international duty with Belgium, but bluntly told reporters that he could not comment on the situation.