A statement from the club on Wednesday said there had been 'a high volume of inquiries'.
The council's Liberal Democrat group leader Steve Darling (Barton with Watcombe) is to meet his Conservative, Independent and Prosper Torbay counterparts to discuss the club's future.
He said: "There is great uncertainty around Torquay United at the moment. It's important that we talk about its long-term future.
"We need to develop a shared statement of intent that the freehold of Plainmoor is not for sale, and also talk about what else the local authority can be doing.
"We need to offer the club an anchor in stormy waters, and our door needs to be open to anyone who is coming forward to support the club. The local authority needs to be using its connections and seeing what opportunities there are to bring in that support for Torquay United.
"We need to come together with a powerful message."
Council leader David Thomas (Con, Preston) told a meeting of the full council last week: "I want to reassure the club and its supporters that we will engage with any interested parties to understand how we might support the ongoing operation of the club."
And he reassured people concerned that the club's Plainmoor ground might be lost.
"The freehold of Plainmoor is held by the council, and we have long held a position that it remains with the council," he said. "Nothing has changed. Our position is still exactly as it was."
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