Alonso's position with British team McLaren, whom he joined prior to this season, have reached breaking point amid the meteoric rise of English teammate Lewis Hamilton.
Developments this week concerning a so-called spying scandal on rivals Ferrari, however, have heaped further pressure on the Spanish two-time world champion.
Marca sports daily said Saturday that Alonso is "considering pulling out for good at the end of the season", but gave no sources for its story.
The report added: "His chances of driving in a competitive team are lacking (...) and he wants to spend more time with his family."
ABC daily newspaper suggested Alonso is set for a return to Renault, with whom he won both of his world championhip titles, in 2005 and 2006.
"The chairman of the Spanish arm of Renault, Olivier Murguet, has affirmed in an interview with that talks on Alonso's return to Renault are at an advanced stage," said the paper.
However a spokesman for Renault Spain attempted to play down the report.
"That was not what was said," the spokesman told AFP.
Having been usurped this season by the talents of rookie teammate Hamilton, Alonso has now become the focus of an investigation by the sport's ruling body the International Motoring Federation (FIA).
The FIA said Friday they would look into the possibility that a dossier containing secret information about Ferrari's tyre and car set-ups had found its way to McLaren.
According to some reports the secret dossier found its way to Alonso, via McLaren team test driver Pedro de la Rosa.
It has been alleged that former Ferrari mechanic, Englishman Nigel Stepney, supplied information about Ferrari's work, notably with Bridgestone tyres and car set-ups, to De la Rosa.
The FIA is set to meet next Thursday.
Alonso meanwhile topped Saturday's morning free practice session ahead of the afternoon qualifying for pole position for Sunday's Italian Grand Prix in Monza.
Ahead of the 13th race of the 17-leg world championship, Hamilton, on 84 points, leads Alonso by five points with Brazilian Felipe Massa on 69.
Last Mod: 08 Eylül 2007, 15:18