The families of Adnan Hajizada and Emin Milli, jailed last year, issued an open letter to Obama asking him to raise the case during talks with Aliyev scheduled for September 24 on the sidelines of the UN General Assembly.
In their appeal, the families called on Obama to come "to the defense of free speech and fairness."
Hajizada, a video blogger and member of the opposition OL! movement, and activist and blogger Milli, were jailed in November 2009 for 24 and 30 months for hooliganism after an alleged brawl in a cafe.
Their supporters say they were victims of an unprovoked attack, imprisoned as a warning to other activists after posting a satirical swipe at the authorities in which Hajizada held a fake news conference dressed as a donkey.
Rights groups say the charges were fabricated and the trial flawed.
with Reuters reporting