The junior club, who play in the East Super League, earned a fourth round meeting with the cup holders courtesy of a shock 1-0 replay win over Championship side Dumbarton, who will be the visitors to Easter Road tomorrow.
With their New Dundas Park ground capable of accommodating only 2,200 spectators, Rose are keen to maximise the revenue from the tie by playing it at the 17,000-capacity home of Hearts. Lennon believes such a switch would make sense.
“I’ve no issue with it, and it probably suits both teams,” the Hibs head coach said. “Financially, for Bonnyrigg, it would be very good. And we are used to the environment at Tynecastle – I don’t know much about the pitch or facilities at New Dundas Park... I’d be in favour of that [playing at Tynecastle], no problem.”
Lennon, meanwhile, has admitted he understands why Hibs fans might have becoming jittery over another twist in their Championship travails that came with the loss to Dundee United last Friday.
The defeat at Tannadice wiped out the three-point lead that Hibs had held over their title rivals who they meet again at Easter Road on 6 January. Lennon’s side remain ahead of United on goal difference but the coach acknowledges fans might be feeling edgy as their team attempts to escaped from the Championship after three seasons in the second tier.
“We are top of the league still but I understand the supporters getting nervy but we are not even halfway through the season and there is more to come from the team,” Lennon said.
“We have been playing very well and at a high level and if we can maintain that then we will see where that takes us. That was our first defeat in a while.”
United have put together an impressive run of form and have not lost in the league since 17 September.