The source said that the five-year deal, worth approximately $7 million per season, has been on the table for "a significant period of time."
If Mankins accepts the contract offer by the midnight deadline, he would be among the highest-paid guards in the NFL.
If a long-term deal could not be worked out for Mankins, his tender would drop from $3.268 million to $1.54 million for the 2010 season.
Mankins was among the restricted free agents who have yet to sign their tenders as reported by NFL Network insider Jason La Canfora. If he does not sign by midnight, New England can lower the amount offered to 110 percent of the previous salary.