The 22-year completed his £30.7m move to Old Trafford on Wednesday.
However, Smalling and Jones will not take Lindelof's arrival lightly and pre-season will become a fiery competition to impress Mourinho, something that Lindelof is not shying away from.
"Of course [I'm ready to fight for my place]," the Swede told MUTV.
"There are some great players here in my position, but I'm here to do my best and try and help the team as good as I can."
"It's always good to have other good players around you because when you have that I think you get better as well."