Webb, who was 22-7 with a 3.30 ERA in 2008, nearly signed a four-year extension with the D-backs early last season, but the D-backs wound up pulling the offer. Since then, there have been no substantive discussions on that subject.
"We met for an hour and 15 minutes," Maurer told MLB.com. "We discussed a number of topics. We discussed Brandon's interest in staying in Arizona and the Diamondbacks' interest in keeping him there. Nothing really came out of it. There was no proposal or contract talks; it was just more about how much Brandon loves playing there."
Byrnes declined to comment on the meeting.
Webb is scheduled to make $6.5 million next year and Arizona holds a club option of $8.5 million for 2010.
"When I said earlier this winter that I expected talks, it was just that, talks," Maurer said. "Not an offer. There has not been an offer and we don't expect to receive one. We don't view that as poor news because Brandon is under contract for two more years with the Diamondbacks and he's happy to be there."
Webb, 29, won the National League Cy Young Award in 2006 and finished second in the voting the past two seasons.
The two sides did discuss another of Maurer's clients, left-hander Mike Bacsik, whom the D-backs are considering signing to a Minor League contract to provide some pitching depth.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.