Subhan Ahmed, chief operating officer of the Pakistan Cricket Board (PCB), said a letter had been sent seeking information on the situation.
"Yes, we have written a letter to the ECB asking them what action they have taken against Broad for comments he has made against Ajmal," Ahmed told AFP.
"These comments are distressing for Ajmal who is upset and wants the ECB to take action," he added.
As an England centrally contracted player Broad can be penalised by the ECB if he is found to have made derogatory comments about his fellow professionals.
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Pakistan spinner Ajmal also currently plays for English county Worcestershire. He took 13 wickets in the Midlands side's recent County Championship win over Essex, including a career-best seven for 19 in the second innings.
This prompted former England captain Michael Vaughan to ignite the row by posting a still photograph of Ajmal bowling during the match on Twitter. He added the caption: "You are allowed 15 degrees of flex in your delivery swing.... #justsaying."
He then commented: "Bowlers can bowl very differently in a lab while being tested compared to needing wickets in the middle."
Ajmal's action -- reported for being suspect in 2009 -- has undergone extensive testing and been passed by the International Cricket Council (ICC).
Under the ICC rules bowlers are allowed to straighten their arm in delivery by up to 15 degrees.
However, English cricket has long been suspicious of 'mystery' spin and innovations such as the 'doosra' (other one) whereby an off-spinner bowls a delivery that turns away, rather than towards, a right-handed batsman.