Hislop told the Radio Times that he thinks the former prime minister would be a great catch for the show.
"I keep saying Blair," he said. "He would be terrific, but for some reason they never book him! It's time, don't you think?"
Hislop also admitted that he enjoyed sparring with Piers Morgan in a previous episode of the show.
"That was car-crash TV," he said. "It was so enjoyable. I was told by people at The Mirror [which Morgan used to edit] that they used to play it on a loop. I haven't seen him since. He was very upset with me."
Hislop suggested that "it's good to take people on" in the show, picking out politician John Prescott as an example.
He said: "You don't want to get too cosy and it's nice to have a frisson - a bit of needle."
Have I Got News For You is taking a break this week for Children in Need, but will return on November 25 at 9pm on BBC One.
> Paul Merton denies Have I Got News is sexist
> Read more TV news