The youngster was impressive in Saturday's 3-1 loss to Arsenal.
He caught the eye as well, with several impressive saves throughout the game showing Allardyce was justified in trusting the youngster.
That form continued his fine showings so far this season, having impressed while on loan with Preston in the Championship, keeping 12 clean sheets in 24 games.
And Allardyce has backed him to have a bright future in the game.
“Jordan has a very bright future ahead of him,” he told safc.com.
“He produced consistent performances in nearly every single game he played for them [Preston] and that was so encouraging from my point of view.”
“I thought he gave a very good debut and we might just see him in the Premier League before the end of the season."
It would not be surprising to see Pickford starring in the first team in future either, with the goalkeeper position very much up for grabs.
Costel Pantilimon is arguably the number one at the Stadium of Light, but he has hardly impressed so far, with three cleans sheets in his 17 appearances in the Premier League.
That kind of form leaves Pickford with every chance of pushing for the position himself, and his impressive display against the Gunners will have gone far to doing just that.