Williams’ goal put Pools on the way to victory at Dagenham last weekend, while Barmby sealed victory over York on his debut on January 25.
The attacking duo have added something extra to Pools side of late, with seven points taken from a possible 12.
Their respective loans from Middlesbrough and Manchester United will run out after Pools’ trip to Northampton a week on Saturday, and, while Pools have a home game with Newport and a visit to Southend before then, Cooper has long stated his aim to keep them at Victoria Park for longer.
Williams is one of a number of Boro prospects currently out on loan, with the aim of impressing new boss Aitor Karanka from afar.
“I was down at Boro last week watching their Under- 21 game and I will be having conversations with the people there regarding Luke and I would like to speak to Warren Joyce (Under-21 coach) at Manchester United about Jack,’’ said Cooper, who has followed Williams’ development at Boro at first-hand during his time as a player and coach.
“Jack was disappointed not to get on at Dagenham on Saturday, but we wondered whether he would start, or put him on, but we proved in the end we got it right.
“When you look at the opposition and weigh up their strengths and weaknesses, then it could be Jack’s chance next time.’’ Yesterday’s reserve game with Sheffield Wednesday was postponed because of a waterlogged pitch in Yorkshire.
That meant Cooper was unable to have another look at Jordan Deacey.
The Bradford Park Avenue midfielder has played three times for Pools’ second XI in recent weeks, as Cooper weighs up the possibility of adding the 19-year-old to the ranks.
“I’ve had conversations with both Jordan and his father and I like what he can do,’’ admitted Cooper, who signed Michael Duckworth from Bradford PA during the summer to good effect.
“The two reserve games we have had against younger opposition he has really sparkled, so we will just have to wait and see.
“With Jack Baldwin moving, we have been presented with an opportunity if we want to bring one or two players in.
“Jordan could be non-contract to have a look until the end of the season as well.
“I will chat with him this week.
“He tweaked a hamstring in the reserve game last Wednesday.
“He’s a nice lad, I’ve a lot of time for him and his dad.
“He has attributes I like, he can handle a ball and is quite creative and, in two reserve games he has showed he can score a goal too.
“At 19, I think there’s certainly some potential.’’