Cowan was one of three additions to a 13-man Australian squad announced for the Boxing Day match with India after the batsmen Phillip Hughes and Usman Khawaja were dumped.
Marsh has played only three Tests and is suffering from back trouble from the recent South Africa tour and is fighting to take his place in the first of four Tests.
The selectors named Marsh, Cowan and Ben Hilfenhaus, along with all-rounder Dan Christian, in their extended squad, but there was no place for the injured allrounder Shane Watson and fast bowler Ryan Harris.
John Inverarity, the chief selector, said the size of the squad was due to the continuing uncertainty about the fitness of Marsh.
Cowan wants to be as well-prepared as possible should the call come to make his Test debut at the age of 29. He presented undeniable selection claims after his fourth century in his past four games.
"You would be silly to prepare expecting not to play," Cowan said in Canberra after the Chairman's XI's drawn match with India.
"I've got no idea how Shaun's back is. I'll assume Shaun will be fit and then it's down to the balance of the side. I'm excited to be a part of the team and hopefully I'll get my chance on Boxing Day to continue a decent run of form."
Cowan hit 109 for the Chairman's XI against India along with two centuries in this season's domestic Sheffield Shield and one for Australia A against the touring New Zealanders. But Cowan stressed that his selection in the Test squad was not purely on the strength of this season's prolific form.
"I've got nine first-class hundreds in the last two-and-a-half years so it's not four hundreds in four weeks and suddenly you're in the Test team," he said. "It's two-and-a-half years of trying to dominate state cricket and I've hit some form at the right time."
Hughes paid for his suspect technique outside offstump, habitually caught in the slips for low scores in the four innings against New Zealand recently.
Khawaja failed to build on starts to his innings and failed to get beyond 38 in his three knocks against the Black Caps. Inverarity said Hughes and Khawaja both needed to produce "compelling performances" to be considered for future Test selection.
Inverarity said Watson and Harris were not considered ready to face India.
"Shane Watson was not considered for selection, as he has not recovered sufficiently, and Ryan Harris has not yet achieved the volume of bowling required to be available for consideration for Test selection," Inverarity said.
Regardless of their selections, Pakistan's allrounder Abdul Razzaq said that with Shane Warne and Glenn McGrath having retired, and Brett Lee no longer playing Test cricket, Australia lack a world-class bowler and will struggle to beat India.
"India are aiming to be the world champions, and they will give a tough time to Australia," Razzaq said.