The Hammers progressed through to the fifth round of the competition last week, with a last gasp header from Angelo Ogbonna seeing them knock out Liverpool at Upton Park.
They were handed a good tie in the fifth round as well, as the draw handed them an away fixture at Championship side Blackburn Rovers on Sunday.
And with his side having sold out their allocation for the trip to Lancashire, Sullivan has promised that his side will be fielding a strong side for them.
“It shows the passionate way our supporters love the FA Cup and this is for a game on live TV. I'm humbled by our support,” he told whufc.com.
“We asked for more tickets from Blackburn, but sadly there was no way they could segregate us and give us more.”
“I'm sure the fans will provide an amazing atmosphere on Sunday and hopefully we will be too good for them, but in football you never know. We will be fielding a strong side.”
It is certainly an interesting decision for the Hammers to target a cup run given how they currently sit in the Premier League.
They are currently 7th in the table, level on points with Southampton in 6th and just one point behind Manchester United in fourth.
That means a place in the top six is very much up for grabs this season and many would have accepted Slaven Bilic focusing on that rather than a cup run.
Instead it seems they are eyeing up a cup run, and it will be interesting to see what team the Croatian names come Sunday afternoon.