Former New York Mayor Rudy Giuliani (R) will announce Tuesday that he will not challenge appointed Sen. Kirsten Gillibrand (D) in 2010, several New York media were reporting Monday night.Giuliani is also poised to endorse the gubernatorial bid of former Rep. Rick Lazio, the GOP’s unsuccessful standard-bearer in the 2000 Senate race.Republicans are still searching for a top-flight candidate to challenge Gillibrand, who has appeared vulnerable in polls. Potential GOP candidates include former state Sen. Michael Balboni; Bruce Blakeman, a top official of the Port Authority of New York and New Jersey; Larchmont Mayor Liz Feld; and attorney Marc Mukasey.