The 26-year-old, who joined the Owls from Derby in 2007, is out of contract in the summer, but is keen on staying on at Hillsborough.
"I love it here. I live very close to the ground, I get on very well with all the players in the squad and I'm working with a top manager in Brian Laws," Tudgay told The Professional Footballers Association official website.
"The club has recently started talks with my representatives so we will see what comes out of it - hopefully something will be sorted out in the not-to-distant future."
Tudgay has had an impressive season so far for the mid-table Owls, scoring 13 goals and he dedicated his good form to the club's team spirit.
"I'm playing with a great set of lads and an excellent coaching staff and we're producing the goods and getting the reward for our efforts."