A Sun investigation - which occupies the front cover and four inside pages of today's paper - alleges that Burnham ally Faiz ul Rasool arranged a meeting with the politician, who is one of four contenders in the race to be Labour leader, after being given a £5,000 donation to Burnham's campaign.
The paper says this may be in breach of Labour's own rules, but says there is no suggestion of Burnham having broken the law.
Myler tweeted last night that the team would be making a complaint to the Independent Press Standards Organisation.
Burnham campaign writing to IPSO about The Sun sting involving 8 month-old baby and hidden cameras— Katie Myler (@LadyMyler) September 10, 2015
Burnham himself has said the same, and his tweet on the matter also expressed concern at the involvment of the baby in the undercover report.
Fully expected to have to contend with a lot of things in this contest but a tabloid sting involving a 9-month-old baby was not one of them.— Andy Burnham (@andyburnhammp) September 11, 2015
The story says that Burnham had asked to hold the reporter's baby when they met, although Myler has questioned on Twitter whether the infant was indeed the reporter's child.
Further tweets from Myler suggested the Sun was "grasping at straws", and explained that the man who The Sun's reported had met with had no official role in Burnham's campaign. She also said the money given to Rasool was not accepted by Burnham's team.
Rasool has had no role, formal or informal, within the Burnham campaign.— Katie Myler (@LadyMyler) September 10, 2015
Our routine due diligence threw up a number of discrepancies and as a result, the cheque was never cashed.— Katie Myler (@LadyMyler) September 10, 2015
Still waiting to hear from The Sun who the 8 month-old baby that was involved in this sting was— Katie Myler (@LadyMyler) September 10, 2015
PRWeek also called Lehal, who declined to comment.
Lehal has also not commented on Twitter about the affair; his last tweet came yesterday as the leadership campaign ended.