Jeb Bush may mount a bid for Senate.

(CNN) - Former Florida Gov. Jeb Bush is considering a bid for the United Sates Senate, Republican strategist Alex Castellanos told CNN Tuesday.

Republicans are urging Bush, the president's younger brother, to strongly consider making a bid for the seat currently held by outgoing Republican Sen. Mel Martinez. The first term senator announced Tuesday he would not run for reelection, setting off what's sure to be one of the most hotly-contested Senate battles in 2010.

Bush, who served as Florida governor from 1999 until 2007 and enjoyed high approval ratings, will take the next month to consider getting into the race, Castellanos said on CNN's The Situation Room. Castellanos is a CNN contributor. Bush also told the Politico he is "considering" getting into the race.

Should Bush decide to run, his presence would add immediate star power to a race Democrats are likely to make their top target in 2010. But the former governor, who has largely remained out of the spotlight over the last two years, could be hindered by his close association with the unpopular outgoing president.

"Let me give him some free advice," Paul Begala, a CNN contributor, said. "Change your name. Run as John Ellis not John Ellis Bush. The Bush brand is probably what croaked Mel Martinez."

According to Florida exit polls on Election Day, just 9 percent of Floridians approve of President Bushs job performance. But Jeb Bush left office in 2007 with approval ratings well over 60 percent, a sign he could be insulated in the state from his brother's unpopularity.