Clark, who has started each of Newcastle’s last eight Premier League games, has a contract with the Tyneside outfit due to run out in the summer.
The Magpies’ league rivals Crystal Palace have been keeping tabs on the defender’s contract situation and are looking to sign him on a free transfer.
However, Newcastle boss Bruce is determined to keep hold of the Ireland international and is pushing for a resolution regarding his contract situation.
With Bruce keen to keep hold of Clark, the St. James’ Park club have already begun negotiations with the centre-back’s representatives over a new deal.
It remains to be seen if Newcastle can convince the Harrow-born central defender to put pen to paper on a new contract at the club.
The 31-year-old joined the Magpies from Aston Villa for a fee in the region of £5m in the summer of 2016.
Clark has helped Newcastle to two wins and two draws from his eight league appearances this season, while also scoring a goal in the process.