Morelos has been linked with an exit from Rangers throughout the transfer window and Lille had a bid for the Colombia international turned down in the summer.
The French side have not been back for Morelos due to financial fair play concerns and Rangers have stuck to their asking price of close to £20m.
It has now emerged they fielded a loan offer from a club in Serie A over the weekend.
The unnamed side offered Rangers a loan fee of around £1.8m in order to take Morelos to Italy for the season.
The proposed deal also contained an option to buy, which is claimed to have been less than the sum Lille offered, which was £14m plus bonuses.
Morelos has attracted interest from several sides but looks set to stay at Ibrox beyond the closure of the transfer window.
The striker has started in Rangers’ last five games as Steven Gerrard continues to count on him.
