The former world number one, now ranked 43, beat South Korean Chung Hyeon 6-3 6-2 in the opening round of the Surbiton Trophy Challenger event.
Murray, 36, skipped the French Open to focus on the grass-court season and hopes to be seeded at Wimbledon.
“It is hard to put numbers on it but I would fancy myself against a lot of them [the top 10],” he said.
Speaking after his first win since claiming the Aix-en-Provence Challenger title last month, the two-time Wimbledon champion drew on his run to last June’s Stuttgart final to show that he remains a threat on his favourite surface.
“Last year I won against [Nick] Kyrgios who made the final of Wimbledon, I won against [Stefanos] Tsitsipas – it is probably not his favourite surface but he is one of the best players in the world,” said Murray.
“I was a set all with [Matteo] Berrettini – who is quite clearly in the top few grass-court players – in the final of Stuttgart before I hurt my abs.”
At the start of Wimbledon 2022, Murray was ranked outside the world’s top 50.
He has been vocal about his desire to be ranked higher in order to avoid facing top players early on in tournaments and give himself a better chance of going deeper at events.
“I’ve got up to 41 in the world and believe I can go higher than that. Obviously I did well here [Surbiton] and in Stuttgart last year and I think I need about 300 points [to be seeded at Wimbledon] so I will have to do well the next few weeks if I want to do that,” said Murray.
“If I have a good tournament at Queen’s, if you make the final or win the tournament there then I would be seeded, but I need to just concentrate on the performances.
“If you start just thinking about points it is not necessarily the best way to look at things. I will just try and win as many matches as possible and see if I can get in there.”
Murray plays with a metal hip after having surgery in 2019 following an injury which appeared to bring him close to retirement.
“I still want to win, I want to compete and see how hard I can push my body,” said Murray.
“The operations I had, I was told I might be able to play again so I just want to see how far I can go.”