The former England international spent last season on loan at Goodson Park from Manchester City and was one of the Toffees’ key performers in a fantastic season which saw them narrowly miss out on a top four finish.
With Barry now out of contract at the Etihad Stadium, the Merseysiders have been linked with a swoop to get him in on a permanent basis, but they face much competition to do so.
The 33-year-old is wanted by Arsenal, Stoke and QPR who are all willing to hand him lucrative contracts to get him on board in the coming months.
If Roberto Martinez is unable to get Barry back, then he may well turn his attention to the impressive Pardo.
The 21-year-old starred for Sociedad last term, making 44 appearances across the campaign.
It is understood that Everton have made tentative enquiries about the youngster, and could well launch a serious offer despite the player having only penned a new contract not long ago.