"Negotiations on this matter have resulted in a deal that will see the Houthis release bin Mubarak tonight," the source, who declined to be named, told The Anadolu Agency without elaborating.
"The hold-up in releasing bin Mubarak has to do with a disagreement over the location of his delivery," the source said.
"Shabwa tribesmen insist that the Houthis return bin Mubarak to the place he was abducted or deliver him to his tribe, which the Houthis reject," the source added.
Last week, Houthi militants kidnapped bin Mubarak at a checkpoint in Sanaa and took him to an undisclosed location.
The Houthis seized control of capital Sanaa last September before moving on to establish control over other parts of the country as well.
The rise of the Houthis has pitted the Shiite group against local Sunni tribes and Al-Qaeda, the latter of which is said to remain active in Yemen.
Yemen has remained in the throes of turmoil since autocratic President Ali Abdullah Saleh stepped down in 2012 following a months-long popular uprising against his 33-year rule.