Loïc Rémy has been told by José Mourinho he will remain at Chelsea and become an integral part of his strike force rather than leave the Premier League champions in search of guaranteed first-team football.

The French striker, 28, feared his time at Stamford Bridge had come to an end following the loan arrival of the Colombian international Radamel Falcao , the former Atlético Madrid and Porto forward who has joined Mourinho’s side on loan from Monaco following a frustrating season at Manchester United.

With Diego Costa Chelsea’s main striker, Remy understandably questioned his future and with the likes of West Ham and Crystal Palace interested in securing his signature, it looked certain he would leave for pastures new.

Yet Mourinho was quick to highlight some invaluable contributions from the Frenchman last season, which helped the Portuguese win the title and stressed that any side wanting to make a move will ultimately be left disappointed.

Asked if Rémy was to leave, the Chelsea manager could not have been any clearer. “No chance. It is open competition between the three [strikers]. That’s our objective, that’s why we want three strikers ready and important.

“Last season Rémy was basically the third forward, but he scored so many important goals for us in crucial moments that gave us crucial points – the goal against Hull City, the goal against Stoke.”

For Rémy himself, the backing of Mourinho despite the arrival of Falcao has been a timely boost to morale before the new campaign. He scored seven Premier League goals from six starts in the title-winning season, ensuring the Chelsea coach had a viable alternative to his first choice attacking options.

“It’s really good to come back for training as I had one month and a half off. Holiday is good but now it’s time to work and to prepare the best way to start the new season,” said the striker who signed for Chelsea from QPR last August for £10.5m.

“We are all thinking about the future. We know that last season was amazing for us with two titles. Now the focus is on the new season and we know that this season is going to be more difficult than the last one because everybody would like to beat the champions. We’re focused.

“I was happy with what I did last season but I think all the players want more. So I want to play more than last season and score more goals than last season. I will see what will happen in the future. But for me the focus is the same, I want to be better than the previous season.”

Falcao will aim to impress his new manager, and team-mates, when he finally arrives at the club’s pre-season North American tour on Tuesday. His fitness, after suffering a knee injury 17 months ago, will be monitored yet Mourinho is keen to have proven back up in the shape of Remy to call upon when needed.

“Falcao for me is one of the best strikers in this league so it’s good for the club to have this kind of player. For me there is no problem it’s just a good thing that he joined us. And it’s going to be good because now we have three strikers and if one of us is injured we know that we can count on three strikers and we know there are a lot of games in the season,” added Rémy.

“At Man Utd he had trouble with injuries I think but before that he was a very good striker and scored a lot of goals so for me it’s good – the same as Didier last season. You learn everything, you learn a lot training next to this kind of player. For me it’s all good to have him and Diego next to me to improve and be a good striker.

“I am flattered that clubs were interested in me but I never wanted to leave this club because I feel really good. Yes, of course I want to play more but I’m sure I can play more here.

“So that’s my target and I just try to make it happen by working hard and show everybody and the manager that he can count on me. For me, my mind is here and I don’t want to leave at the minute. For so many reasons I want to stay – because we won two titles and I’m sure we’re going to win more titles this season, so for me it is really exciting. I want to be a part of this project and there is no reason for me to leave now.

“I know that this season there are a lot of games and I will have my chance and now I have to be ready to be not injured and to be ready at the good time.

“Can I be first choice? Impossible is nothing. I know that Diego is a really good striker and scored so many goals so at the minute Diego is ahead, the No1 choice I think. But for me I think in football, things change really quick so I never give up and you never know.”