The controversial England fly-half has been the subject of repeated disciplinary problems since joining the Melbourne Rebels for this year's Super 15.
Most recently, the Rebels claimed to have "lost confidence" in Cipriani for a breach of conduct that saw him stay out late after a match for a second time and fail to attend training.
Searching for an early end to his two-year contract, Cipriani has identified Bath - who are looking to recruit a fly-half to replace Butch James - as a possible destination.
"We have been contacted by Danny Cipriani's representatives, but he's not top of our list," Blofeld told The Bath Chronicle.
"The approach came at the last minute. Obviously Danny is a very talented player but we don't know what has happened in Australia yet.
"We didn't want to go off-strategy and sign somebody at the last minute.
"But he is someone we have looked at before and somebody we could look at again.
"(Director of rugby) Ian McGeechan already knows him well."
Meanwhile, New Zealand fly-half Dan Carter has confirmed he was contacted by Bath to discuss the feasibility of joining the club.
"I was quite flattered with some of the figures I was getting out of France and the UK," said Carter, who on Wednesday agreed a new deal with Canterbury.
"There were a few good offers - from Racing Metro, Perpignan and even Bath were in there as well."
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