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. "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 added: "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 said. "What you don't see is the amount of effort and time he puts to keep in peak condition."
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.
"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."
Source: PA
Source: PA