Jamie Smith could line up for England’s white-ball team against Australia next month after the gloveman impressed in whites once again, setting up a first-innings lead against Sri Lanka at Old Trafford. Smith hit his third half-century in four Tests as England closed day two on 259 for six, 23 runs ahead of Sri Lanka.

The 24-year-old walked in with the hosts not looking entirely comfortable at 125 for four and proceeded to finish the day unbeaten on 72, his mind possibly wandering to a maiden Test century on Friday.

Related: Jamie Smith eases England into lead against Sri Lanka on rain-hit day

He may also have another format or two to think about soon after Marcus Trescothick, England’s interim white-ball head coach, said Smith may feature against Australia in September.

The final day of the Test series against Sri Lanka is scheduled for 10 September, with England and Australia beginning a three-match T20 series the next day. A five-match ODI series between those sides follows the T20s. Smith made his 50-over debut for England last year against Ireland but remains uncapped in the 20-over format.

“We’ve seen enough of him playing for Surrey in the T20 comp or other competitions,” said Trescothick, who is also an assistant coach for the Test team. “The way he’s come in and taken to international cricket is probably the most important part of that. He just seems very suited to playing international cricket.

“They’ve got a busy schedule doing this. Whether he plays some of it [the series against Australia] or all of it, I don’t know. We’ll wait and see and work out what squad we’re going to pick.”

Trescothick was asked whether he would be interested in turning his interim role with the white-ball setup into a full-time position. “It’s not something I ever thought about before until I got this opportunity,” he said.

“And I’m not necessarily thinking any further ahead than the end of the Australia series. I’ve been very much focused on the job we’re doing here.

“You plan your winter: we go to Pakistan, then New Zealand [for Test tours]. I’m so ingrained in that at the moment that I’ve not really sat down and said, ‘This is where I’m going to go, this is what I’ll try and do’.

“I’m looking forward to the opportunity, for sure. I’m really excited about doing the job and then we’ll work it out a little bit more from there.“