The popular former City midfielder is enjoying his fourth season with the Toffees and is approaching his 36th birthday.
But Barry, an integral member of the City side that won the Premier League and FA Cup, could still be a threat to his former employers according to Toure.
“I know my former team-mate Gareth Barry is going to be immense and run everywhere,” said Yaya.
“They are a very compact team, but we can’t let the gap get any bigger between ourselves and the leaders so we have to go to Everton and win if we’re to remain in the title race this season.
“I’m expecting 90 minutes of fight. We know how difficult it is to play there – in my time at City we’ve only won twice in eight games at Goodison Park – but I think it will be a great match.
“They drew with us 1-1 at the Etihad but that’s a game we should have won.
“They are strong on their own ground and are on a good run so we need to play really well to come away with something.
“Three points – that’s all we are going for this weekend. In my opinion we just need to forget that we are trailing behind Chelsea. We know how difficult it’s going to be – all we have to do is keep winning, keep the pressure up and hope the teams above us drop points.”
