Westwood, 30, only joined the Owls in the summer after being released by Sunderland, but his impressive displays for Stuart Gray's men are attracting interest.
The Republic of Ireland was linked with Liverpool as Brendan Rodgers seeks another goalkeeper with Simon Mignolet and Brad Jones both strugglined this season.
Yet now, their Merseyside rivals could join the race, with Roberto Martinez also needing to sign a goalkeeper at Goodison Park.
The Toffees have seen Tim Howard struggle this season, and now with the United States international out injured, Martinez has been forced to use backup stopper Joel as his first choice, so a deal for a goalkeeper would make sense for Everton.
Westwood's rise from the scrapheap to hot property has been surprising to say the least, but the goalkeeper told The Star last week that he isn't interested in leaving Hillsborough.
"I’m really happy to be here. I’m enjoying my football and Sheffield Wednesday is a fantastic club to play for," said Westwood. "I’m delighted with how things have gone and really happy to be playing football again."
"I had to kick-start my career again, which I think I have done and long may it continue. Sometimes things just fit. The fans have taken taken to me. I have taken to the club. I’m happy and have really enjoyed it," he added.
So, no matter how much the Merseyside rivals, they may not be able to tempt him back to the Premier League - yet.