The Dane has made a good impression since returning to the pitch after suffering a cardiac arrest during the Euros, with his all round play and professionalism instantly lifting the Bees throughout the second half of the season.
Brentford confirmed they have opened talks with Eriksen, who created four assists in his short spell in West London, and hope to extend his stay beyond this summer.
But Gary Neville says he should look at Liverpool, as he would be a good signing for Jurgen Klopp’s men and the way they play.
The now Sky Sports commentator told Metro: “I think Eriksen will be picked up by a big club.
“But okay, maybe he’s showing loyalty, because of what Brentford has done for him.
“But listen here, if you’re a top six club that has a three-man midfield, they’re looking for a player who will be able to come in and play 30 games as a squad player ... he will be able to play for Manchester City, he will play for Liverpool.
“He will be able to play for all the teams in the top six in this country.
“I’m not saying he would start inside every week, but he would be able to enter.
“Keep in mind what Shaqiri delivered for Liverpool in two to three years.
“If Liverpool are looking for a midfielder who will be able to replace, for example, Thiago, who tends to be injured, why not look in Eriksen’s direction?.
“Why should one not be interested in picking him up for two seasons where he will be able to deliver a job?.
“He’s terrific. He is amazingly professional, he is an excellent player and he has incredible quality in his ball game.
“Brentford played here [at Old Trafford, ed.], And yes, it was one of the matches that United won.
“But some of Eriksen’s passes in that match were of another world. At the time, I was just thinking about it ... but Liverpool need midfielders.
“They need quality people who can put the attackers on stage. And if we are to be fair, why not pick up Eriksen?”
The Dane has four assists and a goal to his name since joining the Bees in January.