Inter Milan are willing to pay £11m plus two bonuses to sign Christian Eriksen from Tottenham this month, according to Sky in Italy.
Inter previously offered £8.5m for Eriksen but Spurs are holding out for their £17m valuation of the Denmark midfielder.
The Serie A club's sporting director Piero Ausilio told Sky in Italy on Monday night: "Christian Eriksen is an important player. We have submitted an official offer and now we are waiting."
Eriksen's agent Martin Schoots will meet with Spurs chairman Daniel Levy on Tuesday to discuss the situation.
Schoots was in Italy last week meeting with Inter representatives as talks continued over a January switch.
Eriksen made clear last summer that he was ready to leave Tottenham, although no move materialised then.
His contract expires in the summer and he has been free to negotiate a pre-contract agreement with foreign clubs since January 1.
Inter, who are managed by Antonio Conte, are also keen to sign Chelsea duo Olivier Giroud and Victor Moses this month.
Ashley Young joined Inter from Manchester United on Friday for a fee of £1.3m plus bonuses.
Inter trail reigning champions Juventus by four points in the Serie A table after drawing 1-1 with Lecce on Saturday.
They last won Serie in 2009/10, when Jose Mourinho guided them to a historic treble, which also included victory in the Coppa Italia and the Champions League.