The 39-year-old is believed to be keen on entering management having been out of work since he and Sam Ricketts left Town in November.
It is understood Whitehead feels his values and beliefs on style of play and football ethos are in line with The New Saints' vision.
He is one of several applicants TNS are optimistic about as the Cymru Premier side go about replacing Scott Ruscoe, who was surprisingly axed two weeks ago.
Whitehead, who made more than 600 senior appearances in a 19-year professional career, joined Shrewsbury as first-team coach in 2019. He worked his way up from the old Third Division and was a Premier League regular for seven seasons with Sunderland and Stoke.
He became assistant manager to Ricketts the following summer but is looking for a No.1 job.
The application period at Park Hall ended last Friday and candidates are likely to be spoken to this coming week.
TNS have said that the appointment will hold a UEFA pro licence badge, the top coaching qualification.
Caretaker boss Chris Seargeant, a former Saints striker, could be given the remaining two fixtures ahead of the division's split before TNS look to make the change.
The New Saints are second in the Welsh top flight and trail champions Connah's Quay by six points, although they do have a game in hand.
Former Wales boss Chris Coleman has been linked with the role but it is understood not to be a candidate.
The Oswestry club are believed to be pleased with the calibre of applicants, which include an elite coach who was youngest Englishman to be awarded the pro licence aged 28, as well as a boss who has enjoyed success in the English Football League and a former Saints defender who has managed in the English leagues.