Cotterill was not involved in the 2-1 win over Slovakia on Saturday, but Rowett hopes he is given a chance to shine.
Birmingham City manager Gary Rowett has told the Birmingham Mail that he hopes David Cotterill is given a chance to shine for Wales at Euro 2016, even if it means attracting the interest of other clubs.
Speculation surrounding Cotterill's future at St Andrew's was growing long before Wales opened their campaign with a 2-1 win over Slovakia in Bordeaux on Saturday - their first appearance at a major finals since 1958 - and is likely to continue after the tournament.
The winger was not involved in that historic win, but was nevertheless delighted by the efforts of his teammates.
Having impressed for his club, Cotterill may well feel he is in contention for the games against England and Russia next week, and City boss Rowett is keen for the 28-year-old to be given a chance to shine in France, even if it attracts admiring glances from elsewhere.
He told the Birmingham Mail before the game: “It’s easy for me to say I hope he doesn’t play. You know what, for him I hope he does play,” Rowett said.
“I hope he plays and I hope he’s brilliant in every game and I hope I have a real problem in the summer.
“In a way I hope he goes away and has a great Euros. But I know he will be ringing me, whingeing like mad that he wants an extra couple of weeks off.
“If it’s easy we will probably give him an extra week off. But he will come back hoping for a big season.”
Even if Cotterill does stay on in the Midlands, there is likely to be a period of upheaval at Birmingham, with reports pointing towards a takeover from Paul Suen Cho Hung.