Boyle used to be on BBC comedy panel show Mock the Week, but left in 2009.
Shane Allen, who moved to the BBC from Channel 4, said: "I'm not going to suddenly stop admiring his unique comic talent because I've switched teams.
"I worked with him at Channel 4 and I admired him, but it wouldn't be my first move to get him on air.
"I want to make sure we have the right vehicle and the right channel and that Frankie would get all the support from the top down.
Aye Write! has sold out a series of events already, including its opening night, and has added two new talks to the programme.
Tickets have gone on sale for two new sessions at the festival next month, which is based at the city's Mitchell Library.
One features a panel discussion of the newly released Cambridge Companion to Scottish Literature, and the other is an appearance by the author of the definitive story of the Clyde steamers.