Canos in action against former Everton defender Sylvain Distin
Canos made his debut in the Reds' final day draw against West Bromwich Albion, having enjoyed a productive loan spell at Brentford.
Canos celebrates scoring for Brentford
The 19-year-old, who arrived at Anfield from Barcelona's La Masia academy in 2013, is set to enter the final year of his contract.
However, it is reported that the two parties are "some way apart" in terms of reaching an agreement.
According to recent reports, Canos will have no shortage of admirers, with Rangers, Watford, Queens Park Rangers and Reading all linked with moves.
A reported price tag of £4 million has been bandied about in some places, and the ESPN report states that it remains to be seen whether Liverpool will return with a renewed offer or opt to cash in instead.
Reds boss Jurgen Klopp, who has handed opportunities to a number of young players during his short time at the club, is reportedly keen to add to his wing options this summer.
According to the Times, the Merseyside club are prepared to use Jordon Ibe as a makeweight in their bid to sign Southampton's Sadio Mane.
Southampton's Sadio Mane in action against Crystal Palace's Pape Souare