Bush was seen chatting with News Corp. head Rupert Murdoch, who has urged lawmakers to adopt a pathway to legal status for immigrants who are in the country illegally.
Two of the last three Republican presidents " Ronald Reagan and Bush's father, George H.W. Bush " also extended amnesty to family members of immigrants who were not covered by the last major overhaul of immigration law in 1986.
Obama's executive order has drawn a withering response from Republicans, but also has laid bare divisions among Republicans over how to deal with immigration. The issue is seen as critical for Republicans ahead of the 2016 presidential contest as party officials work to attract more Hispanic voters.
Bush reiterated his interest in a presidential run on Monday.
"I'm thinking about running for president. And I'll make up my mind in short order " not that far out in the future," he said.
"I don't know if I'd be a good candidate or a bad one," Bush continued. "I kind of know how a Republican can win, whether it's me or somebody else, and it has to be much more uplifting, much more positive, much more willing to be practical..."
The comments come as Bush works this week to keep his public profile high.
Earlier in the day, he attended a Capitol Hill fundraiser for Republican Senate hopeful Bill Cassidy, who faces incumbent Democratic Sen. Mary Landrieu in Saturday's runoff election in Louisiana that could increase the Republicans' new majority.
On Tuesday, immigration may come up again as Bush addresses the annual luncheon on U.S. Cuba Democracy PAC in Miami. The organization is a political action committee that advocates a tough stance on Cuba.
Bush, whose wife is Mexican, told the CEO Council that he supports a nation in which people ultimately find no need to identify their cultural origin.
"That is the America we should aspire to " not the one where we're dividing ourselves up to find where we are different," Bush said, "but the fact that you're from a different place or you've got a different origin is totally irrelevant."