Ba moved to Stamford Bridge from Newcastle in a £7m deal in January to support Fernando Torres, scoring six goals in 22 appearances as Chelsea secured a third-place finish in the Premier League.
But he faces extra competition next season following Romelu Lukaku's return from his loan spell at West Brom, while Mourinho is also keen to sign Manchester United's Wayne Rooney, for whom they had a bid turned down last week.
But Ba said: "I will stay. I think we need competition and we welcome the best players in this club.
"More competition is going to make me better anyway. All players want to play, not only centre forwards.
"We will all work in the same direction, for the club, to try and win the games."