The same report also suggests that Manchester United are unlikely to sign the young Holland international as Louis van Gaal feels he already has enough quality players in the same position.
Unless Juan Mata or Angel di Maria leaves, there will be no room for Depay at Old Trafford and Van Gaal has no plans to sell either the Spaniard or the Argentinian this summer.
That has given Rodgers hope that they can convince the 21-year-old to join Liverpool this summer. PSV are willing to sell and have told the Reds that they will need to start the bidding between £15-£18million.
The final price could be considerably more than that as several clubs remain interested in signing the forward this summer. One of those clubs is Paris Saint-Germain, who may well be the favourites.
Liverpool look like they won't have Champions League football next season and that could be key to bagging the signature of Depay. PSG will almost certainly qualify for Europe's top tier competition and can also offer him the chance to play with the likes of Zlatan Ibrahimovic and Edinson Cavani.
Depay has emerged as one of Europe's brightest talents since Van Gaal gave him the chance to impress at last summer's World Cup. He has scored 20 goals in this season's Eredivisie and is currently leading the race for the golden boot.
That has given many hope that he will eventually move from a wide position to a central striker role, which leaves one wondering why Manchester United are not interested.
The next Van Persie?
Robin van Persie has been linked with a move away from Manchester United after a frustrating season under Van Gaal. Depay could be considered as a potential replacement.
He is quick, strong and a clinical finisher; all the hallmarks of a Premier League striker. However, Van Gaal is probably looking for a more established name like Cavani to replace the ageing Dutchman.
Do you think Louis van Gaal is right to be dropping his interest in Memphis Depay, even if it means he MIGHT join Liverpool?
Give us your opinion in the comment box below!
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: http://gms.to/writeforgms