Downing knows the value of the League Cup more than most having appeared in its final with each of his three previous clubs.
And Downing - who made his first Hammers start against Newcastle on Saturday but admits he is some way short of full match fitness - is determined to take every chance to make an impression.
Downing told the Hammers' official website: "For me personally I just want to keep playing and get a good run at it.
"The squad is obviously not massive so I expect everyone will be involved and the gaffer might change around a few.
"A lot of teams disregard the League Cup a little but I always think if you go strong in it, you've got every chance."
Allardyce has intimated he will make wholesale changes, with Ravel Morrison set to be handed his first Hammers start.
Morrison played for the last 15 minutes of Saturday's goalless draw at Newcastle, and Allardyce said: "Ravel is an emerging talent and we've very pleased with what he did in pre-season for us.
"He is an exceptional talent who we hope we can nurture into the fray. Some people might say sticking a player on at that late stage might be risky but we've got to do it at some stage."