The 28-year-old has featured in all of Everton's nine league games in a turbulent start to the season that resulted in Koeman being sacked. Unsworth said Everton were eager to tie Gueye down on a long-term deal.
"I believe we are very close which is fantastic news for Everton, the fans and for me because he is a top player," Unsworth told a news conference on Friday.
"I have watched his performances over the last 18 months and the season he was at Aston VIlla. To tie him down here for a number of years is fantastic. He is a good guy as well, really humble and he is going to be a top Everton player."
Unsworth's first game in charge of the senior side ended in a 2-1 League Cup loss by Chelsea in midweek. The former Everton defender said that although there were positives from their second half performance, they needed results quickly.
"This is Everton Football Club - it's all about results. We expect results, we expect a certain level of performance," he said.
"We got that the other night (against Chelsea). We have to back that up with a couple of wins quickly, not for me but for the club.
"We will do our homework on Leicester... pick a team to win the game with the individuals we have available. It is not difficult at all when you are working with top talent."
Unsworth said midfielder Ross Barkley, who is out of action with a hamstring injury, was three to four weeks away from a return.
Everton are 18th in the table with eight points from nine games while Leicester, who appointed Frenchman Claude Puel as manager on Wednesday, are four places above them.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
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