Totti is in the final year of his current deal with the Giallorssi, but Roma are keen to tie their talisman down to longer terms, but only on a reduced salary.
The 36-year-old is thought to have agreed a substantial drop in wages for a two-year extension at the Stadio Olimpico and will put pen to paper on the deal imminently, according to the Gazzetta dello Sport.
Any official announcement on Totti's future will reportedly be put on hold until later this month, to allow Roma president James Pallotta to fly in from the USA.
Totti's deal also includes plans for when his playing career comes to an end, with a five-year agreement for the forward to take up an ambassadorial position or pursue a coaching career if he wishes.
New Roma boss Rudi Garcia has made Totti an integral part of his plans since arriving in the Italian capital this summer, using him in successive Serie A wins early in the campaign.