Howe is expected to be a target for Championship high-fliers Doncaster Rovers should former Cherries manager Sean O'Driscoll take over at neighbours Sheffield United.
Sources in south Yorkshire suggest O'Driscoll would probably recommend Howe to replace him at the Keepmoat Stadium if he were to head to Bramall Lane.
O'Driscoll is currently the bookmakers' odds-on favourite to fill the vacancy created last week following Gary Speed's appointment as manager of Wales.
Howe, who worked under O'Driscoll for around 10 years at Dean Court, has also been linked with Sheffield United and is priced at 10-1 by Victor Chandler to replace Speed.
Cherries' rivals Bristol Rovers, one of the more financially stable clubs in League One, are also in the market for a new manager following the recent sacking of Paul Trollope.
Howe has already rejected overtures from Peterborough and Southampton to remain loyal to Cherries, the 33-year-old having proved his credentials in his first management post.
However, his impressive record at Dean Court will not have gone unnoticed by chairmen up and down the country and could leave Cherries vulnerable to an approach.
Howe, who is six months into a three-year contract, is currently the 28th longest-serving manager in the country and, arguably, the most successful in the lower leagues.
Asked whether he was concerned Howe could be targeted by a managerless club, Mitchell replied: People have phoned me and commented on various vacancies and Sheffield United was one of them.
But, as far as I'm concerned, Eddie is contracted to us and I hope he's enjoying his time here. I'm sure he will see out his contract and maybe further. Unless we are approached, it is not for us to presume.
We are not looking to lose anybody else in the near future. We have lost two strikers, which I think was unavoidable. I don't see a situation where we would be pushed into anybody leaving the club. We still have a good chance of being in the play-offs and I don't want to diminish that.
That would be the case with everybody that works at the club. I don't see any desire to lose any of the playing staff or managerial staff between now and the end of the season at the earliest.
Meanwhile, Mitchell was quick to scotch an unsubstantiated rumour that he had entered the dressing room to voice his displeasure towards Howe's players at their display during the FA Cup defeat at Notts County six days ago.
I don't think any of the supporters or players were too excited about what happened and the way we went out, said Mitchell. We lost 3-1 and it was disappointing. It was a long way to go to be disappointed.