The winners of next Tuesday’s replay between the Jambos and Partick Thistle, following the 1-1 draw at Firhill on Monday night, will face the Highland outfit in the last four.
And Robertson reckons Hearts could push for the tie to be played at the home of their Edinburgh rivals.
Speaking on BBC Sportsound on Wednesday, Robertson said: “You want the semi-final to go ahead at Hampden but you have to look at it from a player’s perspective and a fan’s perspective – you want a bit of atmosphere.
“We don’t one hundred per cent know [the semi-final] will be at Hampden. It’s a strange one.”
Robertson, who played 513 times for Hearts over two spells, reckons the Caley Jags will take a maximum of 3,500 to any semi-final.
He continued: “If it’s Partick Thistle, they’d probably take maybe six, seven or eight thousand so it would look pretty sparse at Hampden.
“Dare I say it, I’m not even sure if Hearts would take a massively big support to Hampden for a half past 12 kick-off.
“If Hearts get through it wouldn’t surprise me if they lobbied for Easter Road and said ‘look, Inverness will fill one stand, we’ll fill three’ but in an ideal world, you want it to be at the national stadium.
“We want to go to Hampden, but I think the SFA are going to have to come up with some creative pricing or something like that because it’s a difficult one.”
Robertson also warned that an early kick-off could impact on the number of Inverness fans attending, adding: “The time is going to be crucial as well. If it’s half past 12, it doesn’t matter who the opposition is, you’re going to ask the Inverness supporters to come down the road. There’s a few things for them to think about.”
Hearts and Inverness have met before at Easter Road in cup semi-finals on more than one ocasion.
In 2013, Hearts reached the League Cup final after defeating ICT on penalties after a 1-1 draw, while 12 months later, nine-man Inverness exacted some revenge, beating Hearts 4-2 on penalties after a 2-2 draw.