The 32-year-old has made a good impression at Oldham since moving to the club in November, and John Sheridan's side are now third in the League One table after their 3-2 win over Rotherham on Boxing Day.
An Oldham spokesman said: "Several other clubs, including some from the Championship, are also after him. We've made him an offer and we're waiting to hear from him. He likes the set-up here and we're expecting a decision next week."
Gregan played 74 times for Leeds since signing from West Brom in 2004, and the defender is believed to have a clause in his Elland Road contract which would activate a payment to Albion on his 75th appearance.