Budge needs to allocate his final wildcard before qualifying starts tomorrow. Former world No8 and 2006 Australian Open finalist Marcos Baghdatis secured one and rising American Jack Sock the second.
New Zealand No1 Rubin Statham, ranked 289 in the world, is the most likely recipient of the wildcard if Murray declines. Murray played in the 2006 Heineken Open, when he was a second-round casualty to Mario Ancic.
He has since gone on to occupy a position in the Big Four and won both Wimbledon (2013) and the US Open (2012) as well as the Olympic gold medal in London (2012).
Heineken Open top seed and defending champion David Ferrer was another to bow out early in Qatar, along with German Philipp Kohlschreiber.
It was only Murray's second match on the tour after a back operation and a four-month absence. for about an hour his lack of match practice had hardly seemed a problem as he took charge.
Then Mayer attacked more, Murray tired, and everything changed.
"It was amazing," said Mayer. "To be honest, in my mind the match was finished. I don't know how I came back. I played fantastic tennis. In the third set maybe he was injured, but I played well."
Murray, however, admitted to no injuries during the one hour 51-minute encounter, and whatever his physical discomfort it did not prevent him playing doubles later in the day.
"I am stiff and sore but that's to be expected," he claimed. "It's more the joints rather than muscles. I have to get used to changing direction and playing at this level.
"I didn't have high expectations because I have not had many matches. I was playing well and moving well at the beginning."
It was nevertheless "a good day", Murray concluded. "I lost two matches but got through without any niggles or injuries."
Mayer, a former top 20 player, slowly imposed himself on the match as Murray became more defensive, and after letting slip two break points for a 4-2 second-set lead, the Scot hurled down his racket and flung away his sweat bands.
He then served a double fault and dropped serve at the start of the third set and was never close to breaking Mayer after that.
"It's normal - you can't be a hundred per cent, you have to play some matches," the German graciously said. "I am sure he will improve round by round in Melbourne."
However, the loss of court time in preparation for the Australian Open, which starts in little more than two weeks, may prove to be the most significant aspect of the setback for Murray.