Marshall left the Foxes to join Rovers two and a half years ago and has watched on in amazement at the achievements of his former club.
The 24-year-old winger played with the likes of Jamie Vardy and Danny Drinkwater, both of whom are now in the England conversation, and has backed his mates to lift the Premier League title.
He said: "I do (think they'll win it)
I keep in touch with a few of the lads and I think they're quite confident
"I'm quite close to Danny Drinkwater
He's doing well and there's talk of him getting an England call-up, so I wish him all the best and hopefully he can get a Premier League title next to his name.
"When I left obviously they were still in the Championship so they've come on a lot
It's nice to watch them play and see them doing well."
While a Blackburn win over West Ham would hardly cause the same ripples that Leicester have done, it would put Rovers into the quarter-finals for the second year in a row.
Last season they took Liverpool to a replay before exiting, and Marshall believes Championship sides should take inspiration from the Foxes' exploits.
He said: "Anyone watching, especially Vardy's story, it gives you a bit of hope and it's good for the teams who will go up this year
Not just trying to stay in the league but maybe pushing on to try and win it
"Leicester have achieved the impossible
They're up there and the more games they keep winning the closer they get
Hopefully we can take a bit of that into Sunday's game."
Marshall has fond memories of the FA Cup having scored for Leicester against Chelsea at Stamford Bridge as a 20-year-old.
He has scored three goals in the competition this season and also netted in Tuesday's 3-0 win against Fulham, which ended Rovers' run of nine league games without a win.
Marshall is one of the players trying to ensure Blackburn do not miss prolific marksman Jordan Rhodes, who joined Middlesbrough on deadline day.
"Jordan was good for us, he got his goals, but we've got lads in now who can score and hopefully they can produce and we can get something on Sunday," he said
Loan signing Danny Graham scored his first goal for the club against Fulham but is cup-tied for this match along with midfielder Matt Grimes
Source : PA