The 24-year-old was linked with a transfer in the close season after a stellar campaign in which he helped the principality club win the Ligue 1 title and reach the Champions League semi-finals.
But Fabinho stayed with Monaco after a possible move to Atletico Madrid fell through due to the Spanish giants' transfer ban.
"Ordinarily, it's my last season at Monaco. Nothing is signed," he said.
"During the transfer window and even a month afterwards it was a little difficult to live with the situation. But I don't think about it anymore, I've turned the page.
"(As for leaving in January) I don't think so. I have had no contact (from other clubs) and I'm secure at Monaco."
Fabinho, who extended his Monaco contract to 2021 last year, hinted that a move to Atletico could still go ahead in June.
But the defensive midfielder's form has been patchy this season in a Monaco side that have slipped nine points behind title rivals Paris Saint-Germain and dumped out of Europe.
"Yes, it's a possibility, but nobody from Atletico has spoken to me or my agent," he added.
"I have to demonstrate that I'm still at the level to play in teams like that. I know that I'm not the Fabinho of last season and it's hard to explain why."
Monaco was depleted as Kylian Mbappe, Tiemoue Bakayoko, Bernardo Silva and Benjamin Mendy departed in the close season, but Leonardo Jardim's side can cut the gap to PSG to six points at Saint-Etienne on Friday, ahead of the Ligue 1 leaders' trip to Rennes the following day.
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