Lansdown was answering questions at The Robins' annual general meeting on Thursday evening and revealed that they hope to offer new deals to some of Danny Wilson's key squad members.
Brian Tinnion (pictured) and Tommy Doherty are keen to receive new contracts for next term, especially if the club earn promotion to Division One.
Tinnion and Doherty are joined by Mike Stowell, Peter Beadle, Liam Rosenior, Clayton Fortune and Ben Cleverley as players who are all out of contract at the end of current campaign.
The chairman also revealed that City will look to offer youngster Leroy Lita a professional deal, as the striker is still under contract to the club's Academy for another year.
On the possibility of new deals being offered, Lansdown said on the club's official website: "We may well be talking to Leroy about a professional contract in the near future.
"We will also be talking to the players out of contract at the end of the season."
Meanwhile, Lansdown added that a Football League tribunal will be convened next month over the alleged 'poaching' of Tony Pulis to become Robins manager in 1999 from Gillingham.
Gills chairman Paul Scally accused the West Country club of making an illegal approach for Pulis to become Bristol City boss three-and-a-half seasons ago.
The Robins have dismissed the Kent club's claims and are prepared to fight The Gills at the tribunal over the matter.
Pulis, now manager of Division One strugglers Stoke City, recently came to terms with The Priestfield club after being sacked for alleged 'gross misconduct' by Gillingham just days before he accepted the Ashton Gate job.
