The 33-year-old striker was used as a second-half substitute in the new manager's first game in charge, Saturday's 1-0 Barclays Premier League defeat at West Brom, as Allardyce attempted to bring a greater defensive solidity to the team he inherited from predecessor Dick Advocaat.
Defoe, who joined the club in a swap deal with Toronto-bound United States international Jozy Altidore in January, played much of his football under the Dutchman wide in a three-man front line, something which did not make the most of his proven goalscoring talent.
Now he is hoping he can force his way into Allardyce's plans and get back to what he does best.
Defoe told the Journal: "Obviously, I can understand the manager coming in and saying he's not too sure if he wants to play 4-4-2
He might want to be more solid in midfield so you don't concede goals, so we'll just see what happens.
"But at the age of 33, you want to play football
I didn't come here to sit on the bench
You want to play football and score goals
I said that from day one."
That said, Defoe is not looking for an escape route from the Stadium of Light as the January transfer window looms on the horizon.
He said: "I don't think like that, I don't sit there and think, 'Well, come January I'm going to go'.
"I've just got to focus on the games, stay positive and, if I play then, I've got to do my best, work hard and hopefully score.
"The manager knows
I'm 33, I want to play games
If you speak to any of the boys, everyone wants to play
Yeah, the manager picks the team - you've got to respect that - but at the same time, it doesn't mean you have to be happy about it."
Source : PA
Source: PA