The Foxes have been touted as one of the relegation favourites this season after securing promotion from the Championship last campaign, but Simpson has backed the team to defy the critics.
Indeed, Simpson, who signed at the King Power Stadium from Queens Park Rangers, says that he would not have contemplated leaving Loftus Road if it wasn't for Leicester's ambition going forward.
In a question and answer session on the club's official Twitter page, he wrote: "I wouldn't have signed here if I didn't genuine believe that [that Leicester will stay up]. Great ambition here."
@lloydy10000 I wouldn't have signed here if I didn't genuine believe that. Great ambition here.— Leicester City (@OfficialFOXES) September 9, 2014
Simpson is yet to make his Leicester debut, but he is considered a smart purchase by manager Nigel Pearson.
The former Newcastle United defender has all the attributes to be a success, even at the top level, and his addition certainly provides good depth for the Foxes at full-back.
Displacing their current option at right-back, Ritchie De Laet, may be a tough ask as he has started the season well, but Pearson can be confident that Simpson will do a job if called upon.
Leicester are full of confidence after a decent opening to their campaign at the top level. Although they are still looking for their first win of the season, their two home games this campaign have given fans confidence that they can compete.
So far Pearson's men have remained unbeaten in front of their own fans after picking up credible draws against Everton and Arsenal.
When they return from the international break, their task of winning their first game does not look any easier, as they will travel to Stoke City before facing Manchester United at home. But if they can get through their challenging start with some momentum still intact, then they will know the points should start to come.
Simpson also answered a number of other questions during the question and answer session, and below are some of the more interesting answers.
@ChappersLCFC Definitely, but got to win a place in the team first. Lots of hard work to get through!— Leicester City (@OfficialFOXES) September 9, 2014
@KidKunny Haven't had one yet! It's my first away game this weekend so we'll see what happens!— Leicester City (@OfficialFOXES) September 9, 2014
@johnfallen I would have come here anyway, but obviously it helps to know a few people when you arrive. Manager convinced me.— Leicester City (@OfficialFOXES) September 9, 2014
@mattdhemsley He's a very good player, like a lot of the lads here. Been well impressed with training so far.— Leicester City (@OfficialFOXES) September 9, 2014