Baxter, the former Bafana Bafana and Finland minder, was introduced to the players on Tuesday, having signed a two-year contract.
"We met with the coach this morning (Tuesday), and we are going to Limpopo with our heads held high," the Bafana goalkeeper said.
"There is a possibility that Baxter will be there to watch our league game against Ajax Cape Town (in Polokwane on Wednesday evening).
"Now is the perfect time to show him what we are capable of.
"It will be almost as if the players will be on trial, to try and impress him for next season."
It was a diplomatic response from the 24-year-old, who had previously favoured a local man to be at the helm, to allow them more freedom of expression on the field, while the club held stringent beliefs in foreign coaches.
Khune, though, had also said that the team would work with any coach the Glamour side's hierarchy saw fit employ.
Chiefs' executive chairman Kaizer Motaung Senior likened Baxter to another Englishman, the legendary Jeff Butler, who led the club to some of their glory achievements two decades ago.
Butler coached Chiefs to numerous cup titles including the 1991 league crown and the 1996 "mini-league" which preceded the Premier Soccer League era.
He went into semi-retirement, leaving Brazilian Walter da Silva to take over for the 1996/97 season.
"Stuart reminds me of Butler. He did not change our style of play," Motaung said.
"In fact, Butler enhanced it, giving players the freedom to express themselves."
Khune added that he was relieved that his team-mates would be approaching Ajax with more confidence having ended a slump that followed the sacking of Serbian coach Vladimir Vermezovic last month.
Amakhosi suffered four consecutive losses before an improved 2-0 league win over Mamelodi Sundowns last Wednesday.
The return of the injured midfielder Reneilwe Letsholonyane added a new spark to the team.
"It was not easy, and we don't want to be remembered as being part of a team that lost a record number of matches in the club's history," said Khune.
"We went out there to try and do our job, it was obviously not our aim to lose games.
"The coaches (Donald Khuse and Doctor Khumalo) and management have played an important role in helping us."
Khune has also shifted overseas ambitions aside to concentrate on his leadership role at Chiefs.
"It's every player's dream to play in Europe, but I've tied myself with a three-year contract with the club," Khune said.
"I'm doing well at home, there is no rush.
"I just have to focus on helping Chiefs and not think about any movements."