The Hoops are looking for defensive reinforcements and Matthews is on Neil Lennon's radar after the Welshman became a free agent this summer.
Matthews wasn't offered a new deal at Sunderland after his three-year contract expired, with the Wearsiders keen to reduce their wage bill after missing out on promotion from League One.
Celtic are desperate for a right-back, and Lennon had considered a move for Middlesbrough man McNair, only to cool his interest after reports emerged suggesting he was a Rangers fan.
Matthews, meanwhile, remains without a club and is well known to Celtic fans after playing more than 100 times for the Hoops between 2011 and 2015.
He won the title in all four of his seasons at Parkhead before moving to Sunderland for £2million but endured an injury-hit time on Wearside and was part of a Sunderland squad that suffered successive relegations from the Premier League and Championship.
Luton Town full-back Jack Stacey is also on Celtic's radar.