The pair were together at MK Dons and O'Riley has been linked with Saints.
Martin told the Daily Echo: "Matty is someone I had a brilliant relationship with when I worked with him.
"I tried to take him to Swansea and it would have been incredible business for them, as it has been for Celtic.
"I stay in touch with a lot of the players I work with. He's on a long list of players that I stay in touch with and watch with pride at what they've gone on to do.
"I really enjoyed working with him but he's Celtic's player and has done brilliantly for them. He's one of their top players so I'm sure they want to keep hold of him.
"He's had a lot of interest from a lot of clubs. I'll always have an interest in Matty whilst I'm managing and he's playing because as a person, he's great.
"As a player, he's top. If my interest at some point then becomes interest to actually work with him again because it's achievable then...
"I think that would be why you and some other people probably think it's clear I want him, because we have a great relationship."
He continued: "But we'll have to wait and see. We are not in a position where we're going to go and spend absolutely huge sums of money on players.
"I think Celtic want a lot of money for Matty as would I, and as any club would if they had one of their top performers.
"So, yeah, we'll just have to wait and see but he's someone that I like as a person and a player - and there are lots of them.
"I'm sure we'll be linked to more that I've worked with. We signed a few here last summer and again now this summer.
"I have a strong relationship with players that I work with a lot of the time, but we will only bring them here if we think they can really help us."