Murray has enjoyed back-to-back tournament victories working with Bjorkman, winning the Munich Open before clinching his maiden Masters title on clay at Madrid on Sunday.
Bjorkman initially joined Murray’s coaching team in March to assist Mauresmo, who works with the Scot for 25 weeks a year.
“He’s going to be with me after Wimbledon, just me and him through potentially right until the end of the year,” the world No 3 told the BBC.
“I think both of us are quite motivated to do that. I haven’t got to spend too much time with Jonas so far but it’s been a good start and I’ll try to keep it up.”
Murray???s first win against Rafael Nadal on clay in the Madrid Masters final, the Spaniard???s heaviest defeat on the surface since 2004, completed the best week of his career according to Sky Sports??? pundit Mark Petchey.
However, Murray has yet to make a decision on his participation at the Italian Open in Rome this week as he continues his preparations for the French Open later in the month.