Reports in Spain suggest that an offer of €4.5million (£3.9m) has been immediately knocked back.
A sale has not been entirely ruled out, but it is being speculated that it would take €8million (£6.9m) to bring Espanyol to the negotiating table.
A number of clubs are believed to be monitoring Wakaso's situation, with the 22-year-old midfielder having impressed greatly since leaving Villarreal for Catalunya last summer.
Swansea are believed to be among those leading the chase, with Michael Laudrup often switching his focus to La Liga in the pursuit of new recruits.
Espanyol have refused to reveal the identity of the club to have made an initial approach, but have made it clear that the terms on offer fall a long way short of their valuation.
Club director Jose Luis Morlanes told Catalunya Radio: "We have received an offer from a European club but we will not sell on these terms."