The attacking midfielder is out of contract at the end of the season and was linked with a move away in the previous transfer window but a deal failed to materialise.
Reports suggest Spurs are willing to listen to offers of £40million for Eriksen in January, half the amount Manchester United were supposedly quoted in the close season, with a switch to Italy or Spain thought to be his favoured destination.
However, Spurs boss Mourinho kept his cards close to his chest when asked what will happen with Eriksen next month.
"My feelings are until I have anything official rather than hypothetical, I will not comment," Mourinho said.
"The only thing I can say is the player is a free agent at the end of the season.
"Of course I've had a conversation with him, but I'm not sharing anything, from respect with the player."
Mourinho was also quizzed on the possibility of turning Giovani Lo Celso's loan move from Real Betis into a permanent deal.
The Argentina midfielder has made 10 appearances this term but only two of those were as part of the starting line-up, with injury problems having blighted his start to the campaign.
Mourinho has no doubts about Le Celso's quality, though conceded he is still getting to grips with life in England.
"I'm doing my work now to try to improve results and get the best out of the players," he added.
"Of course, Giovani is in Europe for a number of years, but France with PSG and then Spain, it's a completely different football world than it is in England.
"So many experienced players arrive in England and the click for them is not automatic. So a young guy like Giovani also needs his time to adapt to the Premier League.
"You could see, even with Mauricio [Pochettino], an Argentinian man like him, easy communication, surrounded by some boys who speak French, he speaks English, so even in those surroundings of support it's not like he arrives here and explodes immediately.
"But we know the good player he is, give him time to develop and we think he is going to be a good player for us."