Aberdeeen have accepted an offer for right-back Michael Hart from Plymouth but turned down the same club's approach for midfielder Chris Clark.
Aberdeen are facing up to life without Nicholson and Hart
With several other players out of contract at the end of the season, Dons boss Jimmy Calderwood confirmed Barry Nicholson had rejected new terms.
However, Calderwood remains positive on the chances of defender Zander Diamond staying at Pittodrie.
Calderwood's contract also expires in the summer.
Strikers Steve Lovell and Lee Miller, goalkeeper Derek Soutar and defender Richie Byrne are all in the same boat.
"We have built up a very good squad in the last few years but every individual has their own choice to make in life," said Calderwood.
"We are starting to be a feeder country for bigger countries which is great in one way but I don't know if it's good for Scottish football.
"And when they come out of contract, every club has their limits on what they can do."
Calderwood, now in his fourth season at Pittodrie, has been offered a new deal but is looking for assurances that he will have money to improve his squad.
"It's not clear cut but until I've actually signed a new contract, leaving the club remains a possibility," he added.
"I hope it doesn't come to that because I want to stay here, but it is how much others want me to stay that is really going to matter.
"We'll see what develops over the next few days.
"The coaching staff and I will see how things go on the player front this week, then decide what we plan to do.
"If they leave it will be a huge blow, I don't see how we could take four players of that quality in during the transfer window.
"We feel we've done well here but it's now a case of seeing how far the directors are willing to take things forward."
Diamond, a former Scotland Under-21 international centre-half, will meet with the club later this week to discuss his future.
Meanwhile, Aberdeen will this week give a trial to out-of-favour De Graafschap defender Dave Bus.
And former Charlton Athletic centre-half Jonathan Kurrant has left the club after only six months by mutual consent.