The Reds try to wrap up a deal for Aspas.
Several clubs have shown interest in the 25-year-old and are prepared to match the Reds £8.6m bid for Aspas – which is the release clause fee written into his contract.
Valencia had been keen on the Spaniard but due to their financial woes would not be able to reach the valuation, although teams from Italy and Germany are also expected to join the battle.
Aspas played a crucial role for Celta this season as they avoided relegation from La Liga against the odds on the last day of the campaign, despite being favourites to go down.
A stunning piece of skill from the Liverpool target helped set up Insa for the only goal of the game in 1-0 win over Espanyol – a result that kept the Vigo team in the Spanish top flight for another year.
In total Aspas has managed 12 league goals in 34 appearances for Celta and has also contributed with five assists.
The striker is a product of the youth system at his current club and has been a regular feature in the first team for the last five seasons.
The Reds will be hoping that the latest interest in their man will not convince Aspas that his future lies away from Anfield, as manager Brendan Rodgers aims to significantly strengthen his side this summer.
Liverpool have already signed former Manchester City and Arsenal defender Kolo Toure on a free transfer and are being strongly linked with Shakhtar Donetsk’s Henrikh Mkhitaryan.