Lukaku joined Inter last summer on a season-long loan from Chelsea after the Italian outfit agreed to pay a £6.9million fee.
The Belgian striker also took a pay cut to facilitate his Serie A return, though his second spell at the San Siro has not reaped the same rewards as the first.
The 29-year-old spent a large proportion of the season on the sidelines with injuries and has made just seven appearances across all competitions.
Lukaku, who has also scored two goals, represented Belgium at the World Cup but only played for a total of 55 minutes.
The Belgian's future is often a hot topic of conversation and that is set to continue going into the second half of the campaign.
According to Italian journalist Di Marzio, Inter are thinking about renewing the loan. He said (as quoted by FCInter1908): "Inter really appreciated the player's desire to return.
"He reduced his salary, he spoke words of love towards the club and I don't think the club wants to dump him. In any case, I think they are considering renewing the Belgian's loan."
Di Marzio also believes the club will be seeking a better deal from parent club Chelsea, adding: "Perhaps the Nerazzurri will ask to renew the loan but not under the same conditions as last summer when they paid eight million [Euros] to have him in Milan.
"I think Inter will try to review the conditions by leveraging the player's desire to stay: the loan will be requested at different amounts. I think this could be the way."