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Leading cricket website Cricinfo believes Hesson is the No 1 candidate for the vacant Bangladesh role.
He is also down to the final three for the Indian coaching role and has been positioned as a potential replacement for Pakistan coach Mickey Arthur.
Hesson declined to comment when contacted for comment yesterday but earlier in the week announced he had parted way with Indian Premier League side Kings XI Punjab.
"I thoroughly enjoyed my time with the Kings XI franchise and wish to thank them for the season I had in charge. Whilst disappointed not to be able to build on the work we did this year, I'm sure success isn't too far away for them."
The shortlist for the Bangladesh role is thought to comprise Hesson, Grant Flower, Paul Farbrace, Russell Domingo and former Sri Lankan coach Chandika Hathurusingha, who was sacked this week following poor results at the World Cup.
Cricinfo reported Hesson was the "frontrunner, with BCB [Bangladesh Cricket Board] president Nazmul Hassan and some directors expressing interest".
However, Hathurusingha, who coached Bangladesh from 2014 to 2017, is also thought to be a favourite of the BCB president.
Hesson's record stacks up very well, though.
He led the Black Caps to a World Cup final in 2015 and enjoyed plenty of success with the team during a six-year stint from 2012 to 2018.
Hesson was contracted through to the end of the 2019 World Cup but left the Black Caps job a year early, citing the desire to spend more time with his young family.