The 19-year-old, whose current deal at Victoria Park is set to expire on January, 4, has impressed for the Pools since joining from Rovers in September, keeping nine clean sheets in 18 starts.
Wadsworth told the club's official website: "We've enjoyed having Jake with us. He's a smashing lad and most importantly he's a very, very good goalkeeper.
"Blackburn have been excellent with us allowing him to come here and I'm sure we can do something that will keep him here for another month."
Source: PA
Source: PA