Bolton boss Owen Coyle, with money to spend, is another admirer and needs to bolster Wanderers' central midfield for the new season.
Lennon knows Premier League teams will be watching his 26-year-old leader - but says he will remain in Paradise.
The gaffer added: "I wouldn't be at all surprised if there was interest elsewhere because Scott was magnificent for us last season.
"He was so important to me and he's my captain.
"However, I would be very unwilling to sell him and I'd look to rebuff any offers for him."