Several national newspapers have reported that the England international, whose current deal is due to expire in the summer of 2016, has put pen-to-paper on a new deal at Anfield worth a reputed ??100,000 per week.
However the club have said it will not comment on the stories regarding the 24-year-old midfielder.
After a difficult first season, Henderson has become a key player for the Reds since his ??20m transfer from Sunderland in 2011 and has captained the team in the absence of Steven Gerrard this season having been appointed vice-captain by Brendan Rodgers last summer.
With the current Liverpool captain set to depart for Major League Soccer this summer, Henderson has been tipped to take up the armband on a permanent basis and a long-term commitment to the club would make him the most likely successor to Anfield legend Gerrard.
The contracts of central defender Kolo Toure and right-back Glen Johnson are also due to expire at Liverpool at the end of the current season and both have been linked with a move away from the club.