Rosenthal said the deal wasn't in jeopardy, but he was scheduled to be introduced as a member of the Red Sox on Tuesday and that never transpired.
Initial reports from ESPN.com and the Providence Journal said that Napoli's physical was scheduled for last Wednesday, with an announcement expected at week's end.
Napoli actually began his physical Monday morning, according to a source. The deal, however, still was not official as of Wednesday morning.
Neither Red Sox general manager Ben Cherington nor Napoli's agent, Brian Grieper, responded to requests for comment.
The Red Sox signed Napoli to be their first baseman, filling a hole left by the Adrian Gonzalez trade last August. Napoli, 31, is coming off a season in which he hit .227/.343/.469 with 24 home runs in 108 games.
Napoli's best season was 2011. He hit .320 with a 1.046 OPS in 113 games in his first season with the Texas Rangers. He also hit a career-high 30 home runs.
After Gonzalez was traded to the Los Angeles Dodgers, James Loney came to Boston and was the team's primary first baseman. In 30 games, he hit .230 with a .574 OPS and two home runs. Loney signed with the Tampa Bay Rays on Dec. 6.