The Danish star has been a revelation since signing for Brentford in January, following his cardiac arrest last summer.
Eriksen is even back in the international frame, scoring for Denmark during the recent international break.
"In any footballer's decision to move clubs there are a lot of aspects," said Bees boss Thomas Frank.
"It will be the same for Christian.
"To be fair, I know Christian quite well and one thing he's good at is just enjoying the moment. And I think he's enjoying it even more.
"So we are not thinking too much of what is going to happen in two or three months' time.
"I'm just very pleased he's playing for us. It's no secret that I want him to continue next season.
"I know Christian is enjoying his football and really enjoying being back. I know I will have to answer these questions until the end of the season, so let's see what will happen."