Allardyce is currently the front runner for the vacant England job.
David Moyes before the match
The Black Cats could be on the search for their next manager this summer should Sam Allardyce depart.
He has been heavily linked with the England job, which is available after Roy Hodgson’s resignation following the disappointing performance at Euro 2016.
Real Sociedad coach David Moyes is pictured before their Spanish first division soccer match against Atletico Madrid
Should Allardyce leave, his departure would come as a big blow to Sunderland, who were hoping to establish themselves as top ten contenders under his leadership.
A number of names would be linked with the job at the Stadium of Light, but according to the Independent David Moyes would be top of their list of targets.
They report that owner Ellis Short has not been put off despite the manner in which the Scot has struggled over the last three years since leaving Everton.
Leicester manager Claudio Ranieri receives the Barclays Premier League Manager of the Season award from Nathan Horner, Barclays Head of Global Sponsorship (L) and David Moyes (R)
Instead, Short is attracted by Moyes’ record of helping the Blues become regular qualifiers for the Europa League and challenge the top teams during his stint at Goodison Park.
He also believes that Moyes provides a pedigree to Premier League success and approaches have reportedly already been made to ascertain his interest in the role.
Real Sociedad manager David Moyes watches from the stands