Vecino is in the final year of his contract at Inter and has only been a bit part player under Simone Inzaghi this term.
Inter are open to letting the midfielder leave the club in the ongoing window, but no move has materialised so far.
And according to Italian daily Gazzetta dello Sport, Everton are among the clubs that knocked on Inter’s door over a potential move for Vecino, but the player turned them down.
The Uruguayan is only open to leaving Inter this month for a club that he considers to be a medium-high level side, playing in Europe.
If he does not receive a proposal he likes, Vecino is content in running out his contract at Inter and leaving on a free transfer next summer.
Everton have already bolstered their backline by bringing in two full-backs while the addition of Anwar El Ghazi from Aston Villa on loan has provided them another option up front.
The Toffees have had to deal with injuries to key players across the board and it remains to be seen whether they will again look for a new midfielder before the window slams shut.