The Senegal international, snapped up from Aston Villa last year for just £7.1m, was one of the more successful acquisitions under Ronald Koeman and the club are keen to tie him down on improved terms.
"I believe we're very, very close [on Gueye's new contract]," Unsworth told the media at Finch Farm this morning. "I don't believe it's signed and sealed yet but we're very.very close.
"That's great news for Idrissa and great news for everybody at Everton because he's a top, top player. I've watched his performances over the last 18 months and the season he was at Aston Villa he was a top player.
"To tie him down here and keep him 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."