The former world number one, who is gradually making his way back from radical hip resurfacing surgery in January, is feeling better with every match he plays, Delgado said Tuesday.
Murray won the Queen's men's doubles with Feliciano Lopez last month in his comeback tournament.
The British two-time Wimbledon champion then entered the men's doubles at the All England Club, and teamed up with Serena Williams in the mixed doubles.
Delgado said no decisions had been taken yet on Murray's next steps on the comeback trail - and whether he might be up to playing singles at the US Open, which starts on August 26.
"We'll have a bit of a chat after this tournament and see how things have gone the last few weeks," the 42-year-old said.
"To play singles at the US Open is five sets, and is a huge step up from what he's done in recent weeks, so that's something we'll have to monitor. So no decision on that for a while yet."
Delgado said the pain in Murray's right hip had largely gone and the challenge was now building up enough strength and speed to start playing singles.
"With each match that he's played, he's felt a bit easier and from that point of view it's good, things have gone well over the last few weeks," he said.
The next big tournaments in the tennis calendar before the US Open in New York are the hard court Canadian Open in Montreal from August 5, and the Cincinnati Masters from August 12.
However, Murray, 32, the 2012 US Open champion, is thus far not putting his name down for any events.
"There's no tournaments that we're planning to be at. It's going to be very much see how he feels, how he keeps progressing, and when he is ready, and feels ready, then we'll think about it," said Delgado.
Murray teamed up with French doubles world number 21 Pierre-Hugues Herbert at Wimbledon.
They made it through the first round but fell in the second to Croatian sixth seeds Nikola Mektic and Franko Skugor. Both matches went to four sets.
"That was another step up, playing best of five sets," said Delgado.
"He was disappointed to lose because they had many opportunities where they could have won that match.
"It was pleasing that he came through that fine, his hip was fine and they just lost some chances rather than his body being a problem."
Before surgery, Murray's injury was so bad that he could not even tie his shoelaces without pain. The operation was as much aimed at a pain-free life as being able to return to tennis.