In a report by the Daily Mail, Coe was criticised for refusing to give up his reported six-figure salary with Nike given the brand's sponsorship of convicted drugs cheat Justin Gatlin.
The article says that at a time when the credibility of athletics is being threatened by the "greatest doping scandal in its history", Coe's reluctance to recognise any conflict in remaining an ambassador for Nike is "sickening".
The piece also refers to the ongoing doping investigation into the Alberto Salazar-run Oregon Project – a group created by Nike to promote American long-distance running. It says that Coe should also step down from his role as chairman of sports and entertainment agency CSM, part of Chime Communications.
A CSM spokeswoman for Coe said: "Seb Coe has structures and processes in place to identify and manage potential conflicts. He seeks regular and independent advice including registering all of his interests on the House of Lords register so they are open and transparent."
In a statement Nike said: "Sebastian Coe is a Nike ambassador. He’s held this role since 2012. As a Nike ambassador, he holds an advisory role with the company."
PRWeek was unable to contact the IAAF.
In various media including interviews with the BBC and The Sunday Times shortly before his election, former Olympic champion Coe was forthright in expressing concerns about doping in athletics, saying he had made "a declaration of war on my sport".