“I’ve been very much focussed on the job we’re doing here,” said Trescothick, an opener who played 76 Tests, 123 one-day internationals and three T20s for England.

“You plan your winter. We’ve got Tests in Pakistan, then New Zealand, so I’m so ingrained in that at the moment. I’ve not really sat down and said ‘right, this is where I’ll try to go, this is what I’ll try to do’.”

On the white-ball job, he said: “I’m looking forward to the opportunity, for sure.”

England have begun the process to find Mott’s full-time replacement, working alongside a recruitment firm. They travel to the West Indies for a white-ball series in November, preparing for the Champions Trophy in Pakistan next year, but there is not thought to be a timescale on the hunt for a new coach.

Kumar Sangakkara, the former Sri Lanka batter who now lives in Dorset and has worked alongside England captain Jos Buttler at the Indian Premier League, has called the job “an exciting prospect”.

Former England all-rounder Andrew Flintoff, who has worked with the white-ball team as a consultant on a casual basis, including at the T20 World Cup in the Caribbean in July, will not be with the squad for the Australia series.

However, England have not ended their association with Flintoff, who is a close friend of managing director Rob Key. He could be used in other roles in the future.

One player in line for call-up to the white-ball squad is wicketkeeper Jamie Smith, who continued an impressive start to his Test career with 72 not out on the second day of the series opener against Sri Lanka at Emirates Old Trafford.

Smith, 24, helped the home side to 259-6, a lead of 23 runs, on a Thursday truncated by the Manchester weather.

“He just seems very suited to playing international cricket,” said Trescothick.

“Whether he plays some of or all of the Australia series, I don’t know. We’ll wait and see and work out what squad we’re going to pick.”