Huddersfield Town are reportedly keen on the Sheffield Wednesday goalkeeper.
Westwood impressed as Wednesday slipped to a 1-0 defeat at Leeds United on Saturday and, according to The Sun on Sunday, is wanted by Huddersfield at the end of his contract this summer.
The Republic of Ireland goalkeeper is understood to be one of the Owls' highest earners, which could affect the club's plans to offer a renewal in a transfer window where money is expected to be tight once again.
But it may not be an issue for Huddersfield, who will be armed with parachute payments on their return to the Championship next season.
And when asked about Westwood's Sheffield Wednesday future at the weekend, Bruce, the Owls boss, told BBC local radio: "Over the next two or three weeks there are big decisions to be made on a lot of players.
"A lot of players have been here a lot of years and I’m under no illusions that we have to make some difficult decisions. But that’s football and you move on.
"But when when you see Westwood and you see the form he’s in and the way he’s been playing then, of course, we’d like him to stay, I would like him to stay.
"But we’ve got discussions to be had over the next, as I said, couple of weeks at boardroom level, which obviously are going to take place for every club in the summer and there’s big decisions to make at our club."
Westwood - who was disregarded entirely by the previous Wednesday manager, Jos Luhukay - is approaching the end of his fifth campaign at Hillsborough.
The 34-year-old was named the Owls' player of the year in two of his four full seasons.
Huddersfield still have goalkeepers Ben Hamer and Joel Coleman under contract next term, although Jonas Lossl could leave at the end of his deal.