After leaving Inter Milan in December, following a cardiac arrest at the European Championship in June last year, Eriksen joined Brentford on a short-term deal in January until the end of the season.
The Denmark international impressed at Brentford, scoring once and providing 4 assista in just 11 games and is now attracting interest from Manchester United.
Manchester United have reportedly handed the 30 year old playmaker a two-year contract but the Red Devils face competition from Brentford.
Neville has already thrown his weight behind the prospect of Eriksen sealing a move to Manchester United this summer.
“I think Eriksen will get plucked by a big club,” Neville said, speaking at The Overlap Live last month.
“He might show loyalty, to be fair, because of what Brentford have done for him.
“I tell you what, if you were any top-six club that were looking at a midfield-three and you wanted a player to go in there and play 30 games for you in a squad-type [situation], you’d [take him].
“He could play for Manchester City, he could play for Liverpool, he could play for any of the top six.
“I’m not saying starting every week, but he could come on. Look at what [Xherdan] Shaqiri was doing at Liverpool for two or three years there.
“If Liverpool are looking for a midfield player to come on for, say, Thiago – who gets injured a little bit – why would you not look at Eriksen?
“Why would you not look to him to come in for two seasons and do a job for you doing that? He’s brilliant.
“He’s a brilliant pro, he’s a great player, his quality on the ball is unbelievable.
“To be fair, Brentford played out here [at Old Trafford], it was one of the games United won, but some of Eriksen’s passing in that game was out of this world at Old Trafford.”