And Sam Allardyce has told the Hammers to show the rock-bottom Foxes no mercy in their survival bid as he looks to engineer the London club's best Premier League finish since they returned to the top tier.
Top-flight action resumes after a two-week break for internationals, with Leicester facing a make-or-break stage of their campaign.
Nigel Pearson's men are rooted to the bottom of the table and are seven points adrift of safety with nine matches remaining, their last league victory having come in January.
West Ham, who are ninth, ended an seven-match winless league run of their own by beating struggling Sunderland 1-0 last time out.
This campaign is West Ham's third in the Premier League since they won promotion in 2012 and Allardyce wants no let-up in the club's attempt to better the 10th-placed finish of 2012-13.
"It's the cruelty of the Premier League when you don't convert the chances you make and for us all in the end it's a results business," he said ahead of the trip to the King Power Stadium.
"Those results haven't gone as well as performances would suggest for Leicester. They're still fighting.
"Leicester will not give up and they've still got great hope that they can get out of trouble.
"You need to point out to your players at this level of football you have to keep your foot on the gas wherever you are in the table.
"The ultimate goal is to have the best season that we've had since coming back to the Premier League."
Leicester's 2-0 defeat to West Ham in December's reverse fixture was part of a 13-match winless league run.
Pearson remains optimistic of a famous escape and feels Leicester must take advantage of the fact that six of their remaining matches take place on home soil.
"A positive motivator for us is that we've got six games out of nine left at home," he said.
"We know that if we perform at our maximum at home, we've still got a chance. Away games against sides near us are very important too.
"We've got to win games and stay positive, but we've got to strike a balance between that and staying in games.
"It's no longer about staying in touch, we've got to make moves. We need to maximise our opportunities at home. That's pivotal."
Pearson welcomes Liam Moore back to his squad following his loan spell at Brentford, but Dean Hammond (calf) and Zoumana Bakayogo (knee) are still out.
West Ham have Winston Reid (hamstring) back, although Enner Valencia (toe) is not fit to play.
