The Uruguayan expressed a desire to leave the Merseyside outfit before the start of the season, with Arsenal trying to test the Reds' resolve with a reported £40,000,001 bid.
However, Liverpool were able to keep hold of the 26-year-old, who has returned to the side in impressive form, netting a hat-trick during Saturday's 4-1 win over West Bromwich Albion at Anfield.
"For me, this is the place for Luis," Goal.com quotes Rodgers as saying. "I still maintain that even if we were in mid-table this would be the place for him to be because this is a massive club, a global institution.
"But as a football club and as a team we are growing, and he can grow with us. Luis has the support of everyone at the club and the love of everyone and because this is a worldwide institution, there is no better place for him to grow."
Suarez has already been linked with a January exit from Liverpool, with Real Madrid named as a potential suitor.