The 29-year old has been in town since Friday, trialing with the Jets, and it is expected that a 10-match guest stint deal will be sorted this week.
Culina confirmed that Jeffers, who last played with Sheffield Wednesday in March, had impressed during his trial and was eyeing a November 7 start against Sydney FC if everything continues to go well.
"We are not too far off," Culina told the Newcastle Herald.
"If we can come to an agreement he has to obtain a visa which takes four to five days.
"At best, if everything goes through, we are probably looking at Sydney FC next weekend."