The 23-year-old has been discussing the Dundee United winger.
The 24-year-old is out of contract in the summer and BBC Sport have reported that Celtic will try to sign the wide man on a free transfer at the end of the season, agreeing a pre-contract now.
And Matthews - speaking to reporters - says he has always had a difficult game whenever he has played against Mackay-Steven, someone he says has been a long-term target of the club's.
He also highlighted three key qualities that make the winger stand out: his pace, trickery and delivery.
AM on Gary Mackay-Steven: “He’s a very good player and think Celtic have been looking at him for a quite a while." (MH)— Celtic Football Club (@celticfc) January 15, 2015
AM: "He’s an out and out winger so if he comes in he will help the team & help us go forward. Always had a difficult game against him." (MH)— Celtic Football Club (@celticfc) January 15, 2015
AM: "“He’s got pace, a trick, a good delivery and scores goals so I would put him up there," (MH)— Celtic Football Club (@celticfc) January 15, 2015
Celtic boss Ronny Deila today confirmed the SPL champions' interest in Mackay-Steven, while also suggesting that Kris Commons and Virgil van Dijk will both stay with the Bhoys until the end of the current season.
Celtic travel to Hamilton Academical in Saturday's early SPL kick-off fresh off the back of a warm-weather training camp in Gran Canaria.
Deila's men will resume their league season in second place - behind table-toppers Aberdeen - although they have two games in hand over the Dons (they will return to top spot if they win them both).