Philippe Coutinho stated his desire to leave via email. The club rejected the request.
On Wednesday, the Reds rejected a 100 million euros bid (£90m) from Barcelona for the 25-year-old, who is out of Saturday’s trip to Watford with injury.
In a statement on Friday, the club’s owners said its “definitive stance” was that “no offers will be considered”.
Speaking at an earlier news conference previewing the league match at Vicarage Road (12:30 BST kick-off), Liverpool boss Jurgen Klopp said the Brazilian would miss the season opener because of a back problem.
Klopp said he was also a doubt for Tuesday’s Champions League play-off first leg at Hoffenheim as he had “not been in training since last Friday”.
Coutinho, who scored 14 goals in all competitions last season, signed a new five-year deal in January that did not include a release clause. He joined Liverpool from Inter Milan for £8.5m in 2013.
Barcelona have also had a bid rejected for Borussia Dortmund’s 20-year-old forward Ousmane Dembele since they sold Brazil forward Neymar to Paris St-Germain for a world record £200m last week.
The German club confirmed they met Barca representatives but the offer did not meet their valuation of the France international.
This article originally ran on BBC.com