Stephen Hourahan, Chafee's press secretary, said the senator was concerned that Alito "wasn't willing to go as far as Roberts" in describing the Roe vs. Wade decision as "settled law."
The two leading candidates in the Democratic primary who hope to take on Chafee have said they would oppose Alito.
A Chafee vote for Alito would open him to attack from the Democrats in a generally liberal state.
But on Thursday, pressure mounted on Chafee to stand by his party when Stephen P. Laffey, a conservative challenging him in the GOP primary, announced his support for Alito. A Chafee vote against Alito, while potentially aiding him in the general election, could help derail Chafee's renomination bid.