The People says positive talks have been held between England midfielder Lampard and the Italian giants. He could even sign a pre-contract agreement with Milan in the next two weeks.
A senior Milan source said: "We are keen to sign Lampard and are hopeful a deal can be done."
But Lampard wants to continue playing at the highest level in Europe.
He is convinced that a move to Milan could extend his playing career and allow him easier access to his two young daughters.