Kommersant quoted a source in the state-owned United Aircraft Building Corporation as saying that last week the Federal Service for Military-Technical Cooperation, Russia's state-run arms exporter Rosoboronexport, the MiG Corporation, and the Algerian Air Force had signed an agreement on the return of the MiGs.
It said the Russian Industry and Energy Ministry had confirmed the deal.
The aircraft are to be returned within the next few months. However, the source said this did not mean that the previous contract has now been torn up, and Russia will offer Algeria more advanced airplanes, MiG-29M2s or MiG-35s.
Rosoboronexport signed a $1.28 billion contract for the delivery of 29 one-seat MiG-29SMT Fulcrum fighters and six two-seat MiG-29UB fighters in March 2006 as part of an $8 billion military-technical cooperation agreement with Algeria.
Deliveries were to be made from March 2007 until February 2008, but Algeria began refusing deliveries from May 2007, demanding that Russia take back the first 15 aircraft it had delivered, citing the "inferior quality" of certain components and units.
In October 2007, Algeria stopped payments on other military contracts pending the return of the MiGs.
Experts suggest Algeria may have opted instead for French Rafale fighters as France builds up its presence in the North African state.
"The Russian [cooperation agreement] breakthrough in Algeria in 2006 provoked a strong backlash in France, especially following the election of President Sarkozy," said Konstantin Makiyenko, of the Center for Strategic and Technological Analysis.