Zaniolo wants to leave Roma this month and the Giallorossi are also keen to move him on.
Roma are looking for a permanent deal though and have not received any proposals which satisfy them so far, with West Ham United seeing an offer rejected.
Tottenham are in talks over potentially signing Zaniolo and, according to Italian broadcaster Sportitalia, will make a decision soon over whether to proceed.
Spurs face extra competition now though as AC Milan are probing a swoop.
AC Milan sporting director Paolo Maldini has been in direct contact with Zaniolo’s agent and the Rossoneri are due to decide on a swoop this month after they face Lazio on Tuesday.
The Rossoneri are not desperate to land Zaniolo now and would be happy to wait until the summer.
Zaniolo was not involved in Roma’s 2-0 win in Serie A away at Spezia on Sunday, with the winger not in the right mental shape to play for the Giallorossi amid his move desire.