With attendances at Test matches across the world on the decline, Gillespie believes the introduction of a 11th playing nation would help the situation.
Ireland have made public their intention to eventually reach full Test status and Gillespie, who took 259 wickets in 71 Test appearances, believes the International Cricket Council (ICC) should make it happen.
"One fantastic way to give Test cricket a lift straight away would be to give Ireland full Test status," he wrote in a column for All Out Cricket.
"It’s something that should happen sooner rather than later from the ICC. Here is a country that is ready to play international cricket and to have its own fully professional cricketers.
"Possibly there would be some issues to get round in their domestic set-up, but if they're given full Test status in the next few years I'm sure the administration in Ireland - which comes across as a very impressive organisation - would make a real fist of it and would produce a team that could compete strongly at international level, given some time and some resources.
"Imagine if Ireland were given Test status: that would be huge news in world cricket, and it would be a massively positive story for the world game.
"The ICC and all the national boards talk a lot about the importance of protecting the integrity of Test cricket. If it is that important, then we should look to improve it, and in my view including Ireland would improve it.
"It's well-documented that Bangladesh have had their struggles, and perhaps this has made the ICC more cautious about accrediting another nation.
"But New Zealand took a long time to win a Test match when they first came in. Zimbabwe struggle both on and off the pitch.
"I think Ireland would be a safer bet; they would relish the opportunity and be a very competitive team in a relatively short space of time."