Lukaku, 30, spent last season on loan with Inter from Chelsea.
The Belgian scored 14 goals in helping Inter to finish third in Serie A and reach the Champions League final.
Ongoing negotiations with Manchester United over goalkeeper Andre Onana could help Inter raise the finance to bring Lukaku back to the San Siro on a permanent basis.
Chelsea are thought to want £40m for Lukaku, with Inter looking for £50m from United for Onana, which the Old Trafford club believe is too much.
With David de Gea gone, Erik ten Hag would ideally like to sign the Cameroon international before they go on a four-match tour of the United States next week.
Chelsea are also travelling to the States next week, although it is not known if Lukaku will be in Mauricio Pochettino’s travelling squad.
Inter Milan initially signed Lukaku from Manchester United in the summer of 2019 for a club record 80m euros on a five-year contract.
After scoring 64 goals in 95 appearances across two seasons, Chelsea signed him for £97.5m in August 2021 – hoping he could hit a higher level than his previous stint at Stamford Bridge between 2011 and 2014 when he failed to score in 15 games.
He started just 16 Premier League games for the Blues in 2021-22 under Thomas Tuchel and returned to Inter on loan last term.
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