Bournemouth's hierarchy have reportedly expressed confidence that Eddie Howe will turn down interest from Everton and West Ham United in favour of staying put at the Cherries.
Everton are on the search for a new boss following the decision to sack Marco Silva, with David Moyes and Leonardo Jardim among the names that have been linked with the club.
West Ham, meanwhile, could reportedly sack Pellegrini should the club lose to Southampton this weekend following a run of one just win from 11 games.
According to The Telegraph, Bournemouth believe that Howe will stick to his promise to remain at the club until the end of the season at least.
Howe, who began his second spell at the Vitality Stadium in 2012, has guided the club from playing in League One to being a stable team in the Premier League.
Now in their fifth consecutive Premier League season, Bournemouth are sitting 15th in the league table.