The 24-year-old is said to have been given the opportunity to sign a new five-year deal with the club despite the midfielder earlier trying to force an exit.
However, with the summer transfer window now coming to a close, the Saints will be looking to ensure his stay at the club for the coming years.
Manager Ronald Koeman has blocked a number of attempts for the Kenya international to leave as he is seen as the key replacement to Morgan Schneiderlin who completed a move to Manchester United earlier in the summer.
Reed admitted that talks over a new deal for the midfielder have already begun as he hopes to keep him at St Mary’s Stadium heading into the future.
“We’ve already tried to start negotiations on that. We’ve offered him the opportunity for a long-term extension,” he told Sky Sports.
“We’d like to tie him down for another five years. Whether that’s possible or not, I don’t know but the opportunity is there to do that.”
He featured 38 times in all competitions for his side this past term, scoring three goals while providing another one assist.