Goal exclusively revealed on August 22 that David Moyes has submitted an improved £35 million bid for the pair, after the Toffees rejected a "derisory and insulting" initial offer worth £28m for the pair a week previously.
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"I’m going to turn the telly off and hope they’re still here come Monday night," he told The Daily Mirror.
"Nobody wants to lose their best players. Every Evertonian is hoping that won’t be the case, but we live in the real world and things happen differently than you want them to.
"It’s always difficult when you’re talking about the money which is being bandied about by the clubs that are interested."
Wigan chairman Dave Whelan confirmed on Sunday that an offer from Everton for midfielder James McCarthy has been rejected, while Goal understands the Merseyside outfit are hoping to seal a double swoop for Manchester City pair Joleon Lescott and Gareth Barry.
"As with any club, no player is bigger than the club," Osman continued. "If someone goes, you move on, you adapt, you find new ways of playing without those players.
"You will end up getting new players in who will make you stronger in different areas. Whatever happens come Monday night or Tuesday morning, we will move on and make ourselves strong."