The 43-year-old, who has appeared in various reality TV shows in his native Colombia, is a popular target of the local tabloids due to his colorful lifestyle.
Santa Latina, a Colombian porn company, made the offer to Asprilla in an open letter on their website.
"Dear Faustino Asprilla.
"For years [we] have followed your successful career, which has made you a national icon invaluable in Colombia.
"We are convinced that the lifestyle you lead and the media controversy it causes is vital so we dared to make the following proposal.
"As you know, [Santa Latina] is an adult entertainment site, and that's why we offer you 20 million pesos for a week as a porn actor.
"This is a unique offering, which awaits your prompt response. We are convinced that with a little training you could exploit another talent all of Colombia knows you have."
Asprilla, a fan-favourite during his playing days at St James' Park, earned 57 caps for his country, netting 20 goals in the process.
