The Reds opened talks this week with the La Liga club over a deal for the highly-rated full-back.
The Spaniard has been chased by Arsenal but snubbed a move to the Gunners as he wants to go to Anfield instead.
Manquillo, 20, was not sure he would get enough first-team opportunities at the Emirates this season.
But the right-back is more convinced Liverpool boss Brendan Rodgers will give him the chance to shine in England.
Liverpool want to land Manquillo on an initial loan deal with a view to a permanent move next summer.
Rodgers sees the Spain Under-20 star as the ideal replacement for Glen Johnson, who has only one year left on his current deal at Anfield.
Johnson, 29, has yet to agree on a new contract and could leave on a free next summer.
That will leave the right back spot up for grabs.
Jon Flanagan is a natural right back but was used on the left side last season in the absence of the injured Jose Enrique.
Rodgers has been unable to land a left back yet this summer so Flanagan could see himself in that position again next term.
The Kop boss has not given up on Sevilla's left-sided defender Alberto Moreno, but the La Liga club continue to play hard ball over the fee and want close to £20m.
