Cox, 49, has been in charge of the Bucks' National League North rivals – where he played more than 100 games between 1997 and 2001– since October 2019.
The former defender, who is based in Nottingham, led Mansfield Town to the Conference title in 2013. He left in 2014 and has since managed Torquay, Barrow and Guiseley, all in the National League.
Cox's Poppies side crashed out at the final hurdle before the FA Cup first round proper last night as they went down 3-1 at Buxton after extra-time in a fourth qualifying round replay.
The Shropshire Star understands the former Notts County man is on the Telford shortlist to replace Gavin Cowan, who was dismissed from the New Bucks Head more than two weeks ago.
It is believed interviews have taken place with candidates including ex-Shrewsbury chief John Askey and former The New Saints midfielder and boss Scott Ruscoe, who are on the final shortlist.
Kettering have enjoyed a fine start to the National North season under Cox. They sit eighth after just two defeats from eight league games and made it to the fourth qualifying round of the FA Cup.
Cox took over the newly-promoted side flailing at the foot of the division in late 2019 and the Poppies finished 19th from 22 in the curtailed 2019/20 campaign.
Sacked Curzon Ashton boss Steve Cunningham was spoken to by the Bucks after he was approached. He was surprisingly axed over the weekend by The Nash after they got wind of Telford's approach. Cunningham said in a statement last night: "We accepted an invitation to have a conversation with another club, as non-contracted individuals we are entitled to do.
"This conversation, along with an emotional exchange after Saturday's FA Cup game, has resulted in an unnecessary outcome."
Telford remain under the interim management of Dennis Greene, who recorded a first win on Saturday, which lifted the Bucks to 18th. They go to Gloucester, in 21st, this Saturday.