Reds boss Rafa Benitez has reportedly been chasing highly-rated Spanish international left-sided midfielder Riera, with the player's agent, Magico Diaz, suggesting this week that they had been scared off by the £16million price tag.
However, while Espanyol's sporting director Paco Herrera confirmed that Riera would not be allowed to leave for anything less than his £16million release clause, he revealed that Liverpool have yet to make any bid for his services.
Espanyol have already seen off Tottenham's advances for Luis Garcia this summer and Herrera is confident that Riera will also stay put.
"No club has been in touch with us at all," he said. "The best thing that could happen is that no player leaves. Right now Espanyol have a fantastic team.
"The club has fixed a price on the player, and we are not going to accept less.
"This is exactly what has happened with Luis Garcia, and this is the strategy that we are going to follow with all."
Meanwhile, there are reports in Portugal now suggesting that Benitez has given up on Riera and will make a swoop for 24-year-old Quaresma, who is also a target of Inter Milan boss Jose Mourinho.
However, the price tag of around £20million could again be the big stumbling block to the Reds having any success in luring the player to Anfield.