The player was born in Johannesburg, South Africa and he is of Swiss descent - having moved to Switzerland at a very young age.
Last season, Untersee was plying his trade in the Italian Serie B for Brescia on loan from Serie A giants Juventus.
According to The Sowetan, Baxter is heading overseas this week to talk to prospective future Bafana internationals as he looks at options to strengthen the national team.
His primary mission will reportedly be in Italy where he will meet with Untersee and convince him to play for Bafana ahead of the upcoming 2018 Fifa World Cup qualifiers.
The 23-year-old was nurtured in Swiss side FC Zurich's academy, before joining Juventus during the 2010/11 season.
Having played for Switzerland youth national teams, Untersee would have to apply to FIFA to change his international ability if he decides to play for Bafana.
Baxter is also going to see players in Portugal and Norway, and it is said that he has no plans‚ as yet‚ to try and persuade Andrew Surman to play for South Africa.
The 30-year-old midfielder, who was also born in Johannesburg, is currently a free agent after parting ways with English Premier League (EPL) side AFC Bournemouth.
Former South Africa Football Association (Safa) chief executive officer Raymond Hack reportedly visited Surman when he was still at Southampton.
However, the former England Under-21 international was not interested in playing for Bafana.