The 29-year old, who can also add Charlton Athletic, Rangers, Blackburn Rovers, Ipswich Town and Sheffield Wednesday to clubs he has played for, will trial with the Jets for three of four days before head coach Branko Culina decides if they will take him for a ten-match guest stint.
But Culina isn't expecting any miracles as he is aware that Jeffers has not played for a number of months after being released by Wednesday in May.
"It's simply a case where the guy hasn't played at a decent level for a long time," Culina told the Newcastle Herald.
"It's what he's done recently that counts and we need to be a bit realistic."
Culina said he will give the one-time capped England international time to settle before putting him through his paces.
"I'll just give him a bit of time to settle in and have a good look at him on Monday and Tuesday," he added.
"It's probably good to give him a couple of days to get over his jet lag.
"If his mobility is good and his touch is OK, he might just be hungry to prove a point. He's only 29."