Wolves are currently struggling near the foot of the Premier League table with goals a major problem for McCarthy's men and Keane, who could have partnered his international team-mate Kevin Doyle, would have solved that.
Moxey says the club were "prepared to push the boat out" to land Keane but he admits the Midlanders never stood much of a chance of landing the 29-year-old.
"We asked about Robbie Keane and I spoke to Tottenham on a couple of occasions," said Moxey.
"We knew what his wages were and we would have done that but he wasn't going to come to us. Almost every loan at this level also comes with a really hefty fee, but we would have pushed the boat out to get Robbie. In the end, though, the opportunity to fulfil a lifetime's ambition to play for Celtic was too much of a pull."
Keane, who made his debut for Celtic in Tuesday night's defeat to Kilmarnock, certainly looked happy to be at his new club late on Monday night, with the 29-year-old Dubliner relaxed and upbeat as he answered questions after being greeted outside by some 3,000 fans a little before midnight.
Financially, it made little or no difference to the player himself where he went but a move to the SPL takes him out the limelight somewhat and represents something of a gamble for a striker whose longer term future still looks decidedly uncertain.
Keane, though, appears to have few reservations about the move even if, like Harry Redknapp, he anticipates his time in Glasgow being relatively short.
"At the end of the day," he said, "I'm here until the end of the season to get games. It's worked out well for myself, Tottenham and Celtic but that's as far ahead as I've thought; I'm looking forward to playing games.
"I could have stayed there (White Hart Lane), sitting on the bench and be a bit part player but people who know me know that that's not me. I'm not the type to sit about and just pick up my money. I love playing football.
"I think it was inevitable that I would play for Celtic some day," he added, "and I'm here now. And I'm coming here at a good age. I didn't want to come here at maybe 34 when I was maybe struggling."
Scottish Premier Winner 2009/10 Win Outright: Celtic 7/2