Longstaff has been a free agent since last year and has been working at Newcastle to recover from a latest injury.
He is now in talks to sign for TFC, says the Daily Mail.
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Longstaff recently told the SportBible: "The club have been unbelievable with me throughout.
They have allowed me to stay around the place to do all my rehab, which means I've got top physios looking after me every day. If I need extra help on the pitch, the staff will always be there.
They'll often ask how I'm getting on mentally, as well, and still treat me like I'm one of their players.
It just shows how good they are as human beings. They've all played the game and had injuries. They know what it's like."