Bowe's current deal expires at the end of the season and the Ireland international has been linked with a move back to his homeland.
The 25-year-old has reportedly attracted interest from fellow Magners League sides Leinster, Munster and Ulster after establishing himself as one of the world's leading wingers.
"I don't think anyone wants to lose a player of Tommy's quality," said Ospreys director of rugby Johnson.
"I don't know exactly the situation (about contract talks), but we are confident of keeping him.
"He's a quality player and where he has come from in the last 18 months has been outstanding.
"He is a valuable contributor to our team and our squad. We are privileged to have him."
Bowe joined the Ospreys from Ulster in the summer of 2008 and has been a key performer for the region ever since, playing in 18 Magners Leagues games, including seven of the Ospreys' eight fixtures so far this season.
He was a central figure in Ireland's Grand Slam winning campaign earlier this year and also started all three tests for the British & Irish Lions on their summer tour of South Africa.
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