Murray battled to a three-set victory over Gilles Muller in Friday's quarter-finals of the Wimbledon warm-up event at Queen's Club and then caught up with Chelsea manager Mourinho for a quick chat and a picture that he posted on his Instagram account.
The 2013 Wimbledon champion has become friendly with Mourinho since using Chelsea's training ground, which is near his Cobham home, during his recovery from back surgery last year.
And given Mourinho's vast success, including leading Chelsea to the Premier League title and League Cup last season, it is little surprise that Murray is keen to get a few tips from the Portuguese coach.
"But I'd love to chat to him about those things to understand what it is that makes him great. The consistency of his success is pretty incredible really."
Murray was below his best against Muller, but he admitted he was still relieved to have put on a winning performance in front of Mourinho after falling flat the last time he was in attendance.
"I said to him that this was a slightly better performance than the last time he came to watch me, which was at the finals last year when I played against Roger (Federer)," he said.
"So, yeah, I met him a few times when I had my back surgery, I did a lot of my training and rehab in the Chelsea training ground near to my house. I met with him a few times and he's a fun guy."
While Murray has a good rapport with Mourinho, he stopped short of grilling the boss about transfers, in particular Chelsea goalkeeper Petr Cech's proposed move to Arsenal.
"It looks like that's pretty much done now. No, I actually didn't ask him about that!" Murray laughed.
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