Wimbledon mixed doubles star Jamie Murray said he would not mind if his brother chose someone else for the task.
Jamie told the BBC: "If I don't get asked that's absolutely fine by me."
Wimbledon singles champion Andy announced his engagement to girlfriend Kim Sears in November last year.
In an interview with BBC Scotland Sport, Jamie said: "I haven't been asked yet so I'm still waiting on that one.
"We'll see. If I get asked: great. If not, then it's not the end of the world.
"I'm sure it'll be a good day."
Jamie said he was hoping to avoid having to do a speech even if he is asked to take on the post, having allowed Andy to forgo the tradition at his marriage to Alejandra Gutierrez in 2010.
"He was best man at my wedding," Jamie said. "And I told him he didn't have to do a speech because I didn't want him to be stressed right through the day and not be able to enjoy it.
"I could do a speech if he wants me to, but I'm not going to be sticking my hand up for the front of the queue."
While few details of plans for the wedding have been revealed publicly, mother Judy Murray told the Mirror the wedding would be held in October, but said she didn't know if it would be in Scotland.
Andy Murray is getting married later this year but his older brother said that, so far, he has not been asked to take on the role of best man.