Ajmal is currently playing 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.
That prompted former England captain Michael Vaughan to post a still photograph of Ajmal bowling during that match on Twitter with the caption: "You are allowed 15 degrees of flex in your delivery swing.... #justsaying."
Broad, currently out with a knee injury, replied by commenting: "This has to be a fake photo?!".
As an England centrally contracted player Broad can be penalised by the England and Wales Cricket Board (ECB) if he is found to have made derogatory comments about his fellow professionals.
Following the controversy surrounding former Sri Lanka off-spinner Muttiah Muralitharan's unorthodox action, the International Cricket Council ruled bowlers could straighten their arm in delivery by up to 15 degrees.
Ajmal's action has undergone extensive testing and been passed by the ICC.
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.
He took 24 wickets in helping Pakistan rout then-world Test number one England 3-0 in their series in the United Arab Emirates in 2012.
