The 25-year-old arrived at Pools last month and has since played and won all four National League games for the club as they climbed to second in the National League table.
And manager Dave Challinor said tying the former Newcastle United right-back down was a ‘top priority’ this month.
While a deal is yet to be officially confirmed, Sterry has agreed to stay at Victoria Park until the end of the 2020-21 campaign, as reported in The Athletic.
But with the National League season currently up in the air and at risk of suspension, any announcement is likely to be put on hold until Pools are satisfied that the season will continue as planned.
On Thursday evening, the club stated that they would be in favour of playing on with funding made available as a grant by the National League (option two) ‘but contingent on a number of details being confirmed and deemed satisfactory.’
Following Hartlepool’s previous National League win over Wealdstone, Sterry commented: “As long as I can keep performing, keep pushing on and improving myself and help the side keep picking up results then I’m very happy which I am here,”
“I’m at home which is a plus so we’ve just got to keep playing.
"The dressing room is really good, the gaffer is good, Joe [Parkinson] is good and we’ve just got to focus on how we can keep improving and keep looking up at the top end of the table.”