Pagan, who coaches TAC Cup side the Northern Knights, told Channel 7 he was still "very keen to coach" and "in the best position of my life with all the experience I've had".
His comments came a day after Richmond's fourth straight loss intensified the pressure on Wallace's tenure, with the Tigers to discuss their coach's future at a board meeting on Tuesday night.
Pagan told Melbourne radio he wasn't trying to sell himself as Wallace's successor.
"I don't ring anybody up and say, 'I want to coach'. People ask me," he told SEN on Tuesday morning.
"I suppose when it's a slow news day, they say, 'We'll ring up Pagan, he'll say he wants to coach again and we'll get a story'.
"In retrospect, I can see how it's portrayed and it wasn't timely for the Richmond football club and Terry, and I've apologised to him and that's life.
"I feel for the people involved in it. I've been through it myself and I can tell you, it's not a pleasant time.
In an additional twist, Pagan currently coaches Wallace's son Brent at the Knights.
He said he contacted Wallace on Monday evening to apologise, and admitted the Richmond coach was upset with the comments.
He also said he would endeavour to speak to Brent at training on Tuesday.
"I said to him, 'If I've caused you any embarrassment or angst, it wasn't meant with any intent. I answered a direct question and I didn't think it would be tied in with the Richmond football club," he said.
"He was terribly disappointed but I apologised and I'll speak to his son tonight and hopefully I can explain to young Brent the situation."
Pagan, who was sacked mid-season from Carlton in 2007, said he was a "strong believer" a coach should be allowed to see out his last year.
"I think all coaches go in with their eyes open. It's a winning and losing business; if you lose too much, you come under heat," he said.
"That's the way it works. Terry Wallace is an outstanding coach. If you were to bring Alastair Clarkson or Mark Thompson in there, you think it would make a difference? Probably not.
"The situation is, it's tough times at Richmond, and it's about leadership."
Pagan said he didn't expect his television comments to be linked to Richmond and was simply stating his desire to coach a third AFL club.
"It's not about me," he said.
"Last night, my wife said, 'You've made a fool of yourself here', and I had a look at it because she taped it for me, and what I said there wasn't wrong, but the lead in, 'Pagan Poised'; I'm not poised.
"Richmond football club is not interested in Denis Pagan. All I said was I wanted to coach."
