|Wimbledon 2019 on the BBC|
|Venue: All England Club Dates: 1-14 July|
|Coverage: Live across BBC TV, radio and online with extensive coverage on BBC iPlayer, Red Button, Connected TVs and mobile app. Full details|
Murray, 32, is still searching for a partner after being turned down by several players including French Open champion Ashleigh Barty.
The Scot will play in the men’s doubles with Pierre-Hugues Herbert as he builds up his fitness after hip surgery.
“We just have to wait and see,” said American great Williams, adding she “likes to be tongue in cheek”.
Williams, 37, has only played five tournaments this year because of a knee injury, although the 23-time Grand Slam champion says she is “feeling better” going into Wimbledon.
“Let’s see how my knee’s going,” she said.
Williams reached the mixed doubles final in four Grand Slams earlier in the career, winning the Wimbledon title with Belarusian Max Mirnyi in 1998, but has not played the format much competitively in recent years.
Former world number one Murray, who won the Wimbledon men’s singles in 2013 and 2016, said he understood the singles tournament was the priority for Williams.
“If the singles players are up for it and want to try and win and be competitive I’m all for it,” he said.
“Serena is obviously a brilliant player, has a great doubles record and is brilliant on grass obviously. She’s arguably the best player ever.”
Laughing, he added: “So she’d be a solid partner.”
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Murray played down suggestions he might decide to skip the mixed competition because of concerns about the wear and tear on his body.
“Everybody wants me to play, my whole team would like me to play,” he said.
“But from speaking to more experienced doubles players who have been in situations where they have been in the doubles and the mixed, if the weather has not been good the matches can end up getting backed up and you play a lot of Tennis over a few days.
“That’s when you decide whether to focus and prioritise on one or you hedge your bets. The weather is meant to be good, I want to play, my team are keen, so it’s most likely I’ll do it.”