Ellington is currently training with Rovers and is looking to secure a loan move to Ewood Park as Watford seek to get the 28-year-old off their wage bill.
He endured a frustrating loan spell at Derby County last season and Allardyce has challenged Ellington to prove he deserves a move to the Premier League.
"I like to try and resurrect somebody," said Allardyce.
"This is a lad with a huge amount of talent and has a really good
CV from his time particularly at Wigan.
"He's only 28 so whatever went wrong, if we can put things right we'll have a real player on our hands, but he has to prove it in the few days he is with us."