The pair are both vying for the right-back spot in Mark Warburton's Glasgow Rangers side.
The midfielder has impressed for Celtic in recent weeks.
Pulis nearly left West Bromwich Albion following a relatively quiet summer window.
Sunderland are struggling in the Premier League at the moment.
Celtic defender Jozo Simunovic has been linked with Crystal Palace and Newcastle United - and Craig Gordon has hailed him.
The England and Tottenham left-back is confident in his side's ability to threaten the top spot.
The Chilean international was visibly aggrieved after being withdrawn during recent games with Ludogrets and Swansea City.
James Milner has been playing in the role.
The former Republic of Ireland midfielder played for the Black Cats between 2001 and 2004.
Celtic have already created a tremendous amount of daylight between themselves and their rivals.