The summer signing is looking to the clash with Cheltenham Town as another opportunity to earn more minutes for his new side after playing just over an hour on Saturday
The England international played just over an hour on Saturday as West Ham followed up their opening-day win over Cardiff City with a 0-0 draw against Newcastle United away from home.
But the 29-year-old, who moved to Upton Park from Liverpool earlier this month, is keen to get more minutes under his belt in the cup.
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"The squad is obviously not massive so I expect everyone will be involved and the gaffer might change around a few. For me personally, I just want to keep playing and get as fit as I can and get a good run at it.
"A lot of teams disregard the League Cup a little bit but I always think that if you go strong in it, you've got every chance.
"Certainly at Middlesbrough and Liverpool we had that and I also got to the final with Aston Villa. I think we should just go for it because a few teams do disregard it."
Downing also looked ahead to the weekend meeting with Stoke City, which he believes his side can use to cement a fine start to the new season.
"We're a little disappointed we didn't get all three points at Newcastle but getting a point is still good," he continued.
"If we can win at home next week, that point looks even better. We'll be up for it and Stoke will come and have a go at us, so I'm looking forward to it."
Downing has won the League Cup with both Middlesbrough and Liverpool during his career and was a beaten finalist with Aston Villa in 2009-10.