Diego Simeone hailed Diego Godin for his "remarkable" career with Atletico Madrid but refused to confirm whether the centre-back will leave at the end of the season.
The 33-year-old is out of contract in June and has been linked with a move to Inter.
Godin has spent nine years with Atleti, racking up 380 first-team appearances, though reports in Spain suggest he will confirm his departure following next week's home match with Sevilla.
Asked about Godin's future during Friday's news conference ahead of the weekend trip to Espanyol, Simeone said it is down to the player to make a formal announcement.
"I don't think it is appropriate to speak on his behalf," he said. "We love Diego so much. He has given and he is giving a lot to us in every single game he is playing.
"His career is just remarkable. We are very proud of his captaincy and if he has to tell something, I believe it is more fair to be him who talks on what can come in the future."
Thomas Lemar is another player who faces an uncertain future at the Wanda Metropolitano, having failed to make the impact desired since joining for a club-record fee of around €60m at the start of the season.
The French winger has directly contributed to three goals in his last four matches, however, and Simeone believes he still has a big part to play for Atletico.
"I think Lemar is a different player - he has some skills which are unique in this squad," he said. "His football is vertical and he is player who will be improving progressively.
"It will depend on him and us to get his best and also to keep it regular during the games, which has been the way lately. He is not just coming sometimes, he is doing 60, 65, 70 minutes. Working in defence, in attack, in the play, dribbling, crosses, things which will make him better player."
Atletico require just one more point from their final three matches to make certain of back-to-back runners-up finishes in LaLiga.
Simeone is confident that a lack of motivation will not be an issue for his players ahead of the games with Espanyol, Sevilla and Levante.
"There are still nine points to be played. It is true we need just one point to get the second position but we face every game in the same way and we want to win the game v Espanyol," he said on the eve of the trip to Catalonia.
"When we compete, we fight for being as highest as possible. We always work to be first, but if you are not able, what logic says is you should try to get second position. That's the regularity we are looking for and this is what we can be happy for.
"Sometimes being third, others second, others champions... it is what it should be with or without Simeone because the history of Atletico Madrid forces us to be that way."