The attacking midfielder joined the Premier League club on a short term contract midway through last season and Brentford have now offered him a long term deal.
According to a report from Sky Sports, the Premier League side are waiting for a response from the 30-year-old playmaker now.
Eriksen returned to action after a lengthy layoff following his cardiac arrest last year. The midfielder has impressed with his performances for Brentford and it will be interesting to see if he decides to stay with the Bees next season as well.
The player has been linked with the return to Tottenham Hotspur as well and manager Antonio Conte has publicly hinted that the Londoners could make a move to bring the 30-year-old back to the club.
The report from Sky Sports claims that Eriksen is keen on playing Champions League football and the comments made by Antonio Conte have got him interested.
The midfielder will be available on a free transfer this summer and he could certainly prove to be a quality acquisition for Tottenham and Brentford.
The 30-year-old has shown that he has the quality to perform at a high level in the Premier League and therefore he could prove to be a bargain for either club.
Eriksen has played under Antonio Conte at Inter Milan and the Tottenham manager knows him well.
Furthermore, the midfielder has spent several years at the London club and he should be able to settle in quickly and make an immediate impact.
The transfer seems a no brainer for all parties and Brentford will be hoping that the player can snub an opportunity to move to Tottenham in favour of staying with them.
There is no doubt that Brentford need a player of his quality next season and he could have an influential role in the side under Thomas Frank. On the other hand, he will have to fight for a starting berth at Spurs.