The West Ham goalkeeper says he admires the Scottish champions.
Indeed, Randolph will face Blackburn in the FA Cup as first-choice shot stopper Adrian sits out.
And he says he wants to enjoy a strong cup run with West Ham. He has experienced a Scottish Cup final before - where he lost to Celtic 3-0. But he says he admires the Bhoys...
The Hammers goalkeeper told the Mail: "I just want to have a good cup run. I’ve never been involved in a team that’s had a good cup run and this season, of all seasons, it would be nice to have a good Cup run.
"There was the Scottish Cup final and we lost 3-0. We lost so it just stayed there. I don’t need to watch that back again. I have a little soft spot for Celtic but it didn’t hurt any less."
Randolph has been told he is definitely starting for West Ham against Blackburn Rovers in the FA Cup on Sunday afternoon.
As for Celtic, they remain in the Scottish Cup but were recently knocked out of the Scottish League Cup.
They beat Inverness Caledonian Thistle 3-0 on Saturday afternoon and the Hammers will hope for a similar result against Paul Lambert's side.
Randolph was impressive in the previous round against Liverpool but two Championship sides have already avoided defeat against Premier League opponents so far this weekend.