The England international has been linked with a move away from the Merseysiders for a while now, with Manchester United thought to be the most keen on a move for the 27-year-old.
However with just a few days left in the current transfer window, Round believes that Baines will be staying with the Toffees for now.
"There are only a few days to go and I don't think anyone is leaving now that's for sure," Round said. "We have quite a strong 16 players.
"His heart is here definitely, he is a local boy. He loves the club, loves his teammates and loves to go out there to play and perform. He has never mooted anything else. Fortunately we have not had any bids. Leighton is here so long may it continue.
"Leighton is a top player, arguably the best or one of the best left-backs in the Premier League and Europe. I think he has shown that on a regular basis over the past two or three seasons. He is consistent and his assist making is always in the top 10 of the Premier League and for a left-back that is very impressive."
Baines joined Everton in 2007 from Wigan Athletic.