Tynecastle officials will not ask the Scottish Football Association to move the tie despite suggestions it could take place at Easter Road.
Tuesday's 2-1 win against Partick Thistle in a quarter-final replay propelled Hearts into the last four against John Robertson's Inverness. Aberdeen meet Celtic in the other tie after eliminating Rangers in their replay.
The semi-finals are scheduled for Saturday April 13 and Sunday April 14 and the Hearts manager Craig Levein expects both matches to take place at the National Stadium. Robertson said last week that he would not be surprised if the Edinburgh club lobbied for Easter Road, but Levein stressed that is a non-starter.
"I would prefer it at Hampden and, if anybody asks me, I'll be telling them I want it to be at Hampden," he told the Evening News. "Sometimes semi-finals in other competitions will be played at other venues, but generally both Scottish Cup semi-finals are played at Hampden. I assume that's where it will be."
Hearts' Betfred Cup semi-final against Celtic last October was moved to Murrayfield to avoid hosting two semis at Hampden on the same day. There is no such scheduling issue this time.
"We had the situation earlier in the season because of a fixture problem and we had to play the Betfred Cup semi at Murrayfield. I don't see that as an issue this time so it should be a day out at Hampden," added Levein.
All four clubs involved must now await news from the SFA regarding which day they will play and which kick-off time they will be allocated. Discussions with television broadcasters are taking place at the moment.