Ba signed from Newcastle in January to support Fernando Torres, but with Romelu Lukaku back from his loan at West Brom and Chelsea's pursuit of Manchester United striker Rooney ongoing, there has been speculation that his time at Stamford Bridge could soon end.
Jose Mourinho has insisted none of his players will be sold, but Ba would fall down the pecking order if Chelsea can successfully recruit Rooney, for whom they had a bid turned down last week.
"I will stay," Ba said.
"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."
Ba scored in the final match of the Asia tour, an 8-1 victory over the BNI Indonesia All-Stars in Jakarta.
Competition for places will resume - without Rooney - next week when the squad reconvene at their Surrey training base ahead of four matches in the United States, beginning against Mourinho's former club Inter Milan next Thursday.
Torres and five other players involved in the Confederations Cup - Juan Mata, Cesar Azpilicueta, David Luiz, Oscar and John Obi Mikel - will join up with the squad after missing the three-match tour to Bangkok, Kuala Lumpur and Jakarta.
Mourinho declared the tour of Asia a success after rapturous receptions in each location, including on the Blues' first trip to Indonesia.
The Portuguese suggested that 10 years ago, prior to Roman Abramovich's revolution of Chelsea, the club's reach would not have been so great.
"It is fantastic for us to see how big this club is becoming," Mourinho said.
"Our winning history is recent. In this club we have had a fantastic evolution and our success has come recently in football terms."
On the field, the players feel they are finding form at the right time, with the season commencing with two home games in four days - against Hull on August 18 and Aston Villa on August 21 - before travelling to Manchester United on August 26.
Defender Gary Cahill said: "It's been successful, it's been good.
"We're going home a lot fitter than we came and I think we've improved game after game. The lads are starting to look sharp.
"The US will be a lot tougher test for us. Hopefully we can kick on again.
"We've got a big squad going over to the US, I'm sure it will be rotated.
"We've got some great competition over there. It will certainly get us to the same sort of level to what we will face in Europe and the Premier League.
"It's all about getting games in now and getting ready for the start of the season."