Prop Thomas, who was recently named in England's RBS 6 Nations squad, is widely expected to join Bath.
Back-row forward and former England Saxons captain Gaskell, meanwhile, has been linked with a move to Wasps.
"'Jamma' and Henry are moving on at the end of the season and replacements are being sought as we speak," Diamond told the Manchester Evening News.
"We're confident that we will replace the lads and we wish them all the best. It's the nature of the beast that while some players want to stay, others wish to move on.
"With both Henry and 'Jamma' it's not a money issue as to why they are moving on - it is purely for rugby/lifestyle reasons.
"There is no rancour or bad feeling, and we'll wish both of the lads good luck when they do move on."
- Sports & Recreation
- England Saxons