Portsmouth insist they never made a move for Molde coach Ole Gunnar Solskjaer.
They were linked with Manchester United legend Solskjaer, but chief executive David Lampitt said: "He (Appleton) was definitely the only man we offered the job to. There were an awful lot of reports about an awful lot of names.
"We appreciate that there was a lot of speculation.
"Some names were right and some names were wrong but I don't think it's the right thing to talk about who was involved."