The full-back has been linked with a move away from Goodison Park but Round says the club have not received any bids and would not welcome any.
"There are only a few days to go and I don't think anyone is leaving now that's for sure," he said. "We have quite a strong 16 players
"His heart is here definitely, he is a local boy. He loves the club, loves his team-mates 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' attitude as well as his performances on the pitch have caught Round's eye.
"He is a really matured into a top-class player who is very good professional as well," he added.
"What you don't see is the amount of effort and time he puts to keep in peak condition.
"And he is a very humble guy who is always willing to learn and wants to know that bit extra, always asking coaches what he can do to do that bit extra to improve, which is why he is where he is."
New signing Kevin Mirallas is another who has impressed Round, who says the striker is likely to make his home debut against Leyton Orient in the Capital One Cup on Wednesday evening.
"He is a very fast, sharp player that gives us a different dimension," Round said. "He will run in behind and he's very alert.
"We have to be a bit careful because he has come from Greek football and in the Premier League it is difficult to settle and it takes bit of time.
"I think we are prepared to give him that time and bring him along gradually.
"First impressions are pleasing and it looks like he will be a very good player for Everton."
Full-back Tony Hibbert is the only injury concern for manager David Moyes, who has picked the same squad for Wednesday's match that comfortably disposed of Aston Villa at the weekend.
The Scot has yet to win a trophy during his 10-year tenure, and that is something Round says they want to address.
"We take this competition seriously, we really do," he said. "It is an opportunity to win silverware."