Carlisle are amongst those chasing the 21-year-old after he made 16 appearances for them on loan last season.
City chairman Adam Pearson believes it will be either be Carlisle or the Tigers who win his signature - if the Magpies decide to sell.
Pearson said: "We're doing everything we can to keep Stuart. We know Newcastle have received a number of offers and our's matches the best.
"We've been assured that if they do decide to sell him, we will have the first option but it might not be as straightforward as that. There are other things to consider. For example, Stuart has family and friends in the Carlisle area.
"At the end of the day, everything depends on what Newcastle decide. It's by no means certain they will want to sell him and if that's the case we're hopeful he will continue his loan spell with us. I want to assure our fans we're doing everything we can."
Meanwhile, left-sided midfielder Dean Keates has joined the club on trial. The 24-year-old has played in around 200 games for Walsall previously, and would be available on a free transfer after turning down a new contract from the Sadlers.