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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.