A national newspaper article today suggested that Cherries' wing wizard had emerged as a potential transfer target for south coast rivals Saints.
But Mitchell was quick to pour cold water on those rumours.
When asked if he had heard from Southampton regarding Pugh, Mitchell told the Echo: No, not at all. And I don't think he would go for £200,000.
I think he's worth a lot of money he's a very good player and he's certainly worth more than £200,000.
Pugh has made a big impression since joining the Dean Court outfit from Hereford United in the summer.
He leads the club's goalscoring charts and has been one of the major reasons behind their climb into the League One play-off zone.
Cherries sold Brett Pitman to Bristol City earlier in the season and Josh McQuoid headed for Millwall last month.
But Mitchell stressed his desire to keep hold of Cherries' latest big asset.
He added: We don't want to lose him and we're not going to lose him, as far as I'm concerned.
I think he's done very well. I think he's a great choice and he has played fantastically.