``They made me a concrete proposal but I am open to other solutions,'' the Italian rider said in an interview published Monday by French sports newspaper L'Equipe.
Basso gave no details. Discovery has been looking for a replacement for Armstrong, who retired after winning his seventh consecutive Tour de France in 2005.
Basso said there was also a chance he would stay with his current team, CSC, or join an Italian team.
``Everything is possible, but at the moment _ and I am being sincere _ I hope that I can continue with CSC,'' said Basso, who is contracted with the Danish team until 2008.
Basso and several other pre-race favourites were excluded from this year's Tour de France after they or their teammates were implicated in a Spanish doping investigation. The riders were alleged to have had contact with a Spanish doctor accused of running a blood doping clinic.
Basso denied the allegations. The Italian Olympic Committee's anti-doping commission said last week that it would recommend to the disciplinary body of the Italian Cycling Federation that the accusations against Basso be dropped.