US Weekly magazine first reported that Hasselbeck was leaving the show. An unnamed source told the magazine's website that she did not attract enough viewers and that her contract would not be renewed.
Deadline.com and the Hollywood Reporter also reported Hasselbeck's departure, citing unnamed sources.
ABC released a statement saying only that Hasselbeck "is a valued member of 'The View' and has a long-term contract."
Her agent did not return calls for comment on the reports.
Hasselbeck, 35, joined the long-running women-oriented talk show in 2003 and is an outspoken conservative, often clashing with former co-host and liberal Rosie O'Donnell.
Co-host Joy Behar, who has been with the program since its debut in 1997, said on Thursday that she would leave the show after the season.
Hasselbeck and Behar host the show alongside veteran TV journalist Barbara Walters, actress Whoopi Goldberg and actress-comedienne Sherri Shepherd.
Hasselbeck, who is married to former pro football quarterback and ESPN commentator Tim Hasselbeck, began her television career as a contestant on the CBS reality series "Survivor" in 2001.
ABC is owned by Walt Disney Co.
(Reporting by Eric Kelsey, Editing by Piya Sinha-Roy and Xavier Briand)