Everton manager Koeman believes Barkley will leave Goodison Park this summer but insists the club will not be hostage to a deliberately late, undervalued offer for the midfielder.
"You have teams like Manchester City and Manchester United who will be stronger than last season, but it is still not the end of the transfer window".
Bet 365 are giving odds of 7/10 for Everton to win against Stoke City in Saturday's clash at Goodison Park.
Everton's last four Premier League campaigns have all started with a draw, with three of those ending 2-2.
"I know the expectations are higher than last season but I always look to be realistic".
Everton also signed Sandro Ramirez from Malaga, who scored an impressive 14 goals in 30 appearances last season. "And if you think it's a really tough start maybe it is different because everybody is not on his best at this stage of the season, the end of the pre-season".
Mark Hughes has warned his Stoke side not to get dazzled in the spotlight of the Rooney show. But, given the Belgian's experience, and this being the opening game of the season, the 29-year-old just might get the nod ahead of the duo.
"We know at home that we have that fantastic support and hopefully we can get a good win this Saturday". Everton have enjoyed a positive head-to-head record against the Potters too.
Having said that I'm backing them to kick the season off with a win against a Stoke side I fear will struggle having lost Marko Arnautovic to West Ham. "He is an important player and he is one of the team that will start this Saturday".
"They've got a good side and they've spent money from letting good players go, perhaps similar to Southampton a couple of years ago. We are looking forward to getting started".