Blofeld said Bath's new owner Bruce Craig brought a crucial "passion" for success to the club.
"The club are actively looking for alternative locations in the city, " said Bath chief exec Nick Blofeld.
Blofeld joins the Premiership club from Epsom Downs Racecourse where he was managing director for three years.
Bath chief executive Nick Blofeld has added his weight to the bid to bring Eastmond to The Rec.
In the early 1970s, Christopher Martin-Jenkins and Henry Blofeld were introduced to the team and are still there today.
Blofeld says the unique pace of cricket will ensure it remains on the airwaves for many years to come.
"We would love to recruit Dan but cannot see that happening in the short term, " Blofeld told BBC Radio Bristol.
He has been broadcasting since 1987 and says his best broadcast moments have been the times spent with Henry Blofeld.
The Norfolk project, which opened in 2007, was devised by two local businessmen Tom Blofeld and Simon Egan and includes treehouses, zip wires, jungle bridges, storytelling, boat trips and marsh walks.
With his deal at Bath due to expire at the end of this season, the Somerset club's chief executive Nick Blofeld admitted on Friday that Hape could be set to exit.
Located within the Bernese Alps, Piz Gloria was still under construction when it took on its starring role as the allergy research institute used by Blofeld to brainwash a group of beautiful women from around the world.
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