Gil has struggled to settle since joining Tottenham last summer and none of his nine Premier League appearances came in the starting eleven.
Antonio Conte has been open to loaning the winger out and Valencia have been in talks with the north London club over signing Gil, who is keen to return to Spain this month.
But the Spanish side were not prepared to pay the financial demands Spurs were initially making.
However, according to Spanish radio programme Onda Deportiva, Valencia have made some progress in the talks and Spurs chairman Levy has lowered his demands.
Towards the end of last week, the total cost of signing Gil on loan for the rest of the season would have been €4m, taking into account a loan fee and his wages.
But Levy and Tottenham have changed their minds and their financial demands have come down.
Negotiations are still ongoing and Valencia are pushing to take the former Sevilla winger to the Mestalla on loan for the rest of the season.
Gil is open to the move and wants to play regular first-team football in the second half of the season.
