The left-back's short term deal ended at the Globe Arena on Monday but he has been offered another contract until the end of the season after some recent impressive performances.
Capaldi has been interesting Scottish Premier League side Aberdeen but McIlroy said: "We have spoken to Tony and offered him a new deal and we definitely want him to stay.
"He has shown his quality in the past few weeks and played a big part in our success.
"We will continue talking and we will do all we can to keep him here."
Source: PA
Source: PA