The Giallorossi legend has asked the club's vice-captain to honour his 30th birthday by committing his future to Stadio Olimpico
Chelsea showed an interest in signing the Italy international in the early part of the close season, while Real Madrid and Paris Saint-Germain have also been linked with a bid for the midfielder.
However, Totti is hopeful that De Rossi will honour his 30th birthday by committing his future to the Stadio Olimpico side.
"Best wishes for turning 30 Daniele, even though you are getting old now and are practically finished," joked Totti in a video message on Roma Channel.
"It will be best if you give us a present rather than the other way around, so stay here at Roma and we will win something beautiful together."
De Rossi has spent his entire career to date with Roma, making over 300 Serie A appearances for the capital club so far.