Barry Axelrod, agent for Matt Clement, said his client is close to making a decision and that the Indians still had a chance to sign him.
"Matt and his wife [Heather] were going to try and figure out what they're going to do later today or tomorrow morning," Axelrod said Thursday afternoon.
The Indians, Boston, Los Angeles and Anaheim are among the teams bidding for the free-agent right-hander. He may also accept the Cubs' offer of arbitration, but Axelrod said that would be used only as a last resort.
"We've told a couple of teams that they're no longer in contention," said Axelrod. "But it's not down to two teams yet."
The Indians have offered Clement, 30, a three-year deal worth an estimated $21 million.
The Indians' offer has not changed since the winter meetings ended Monday in Anaheim, Calif.
"The three-year offer is still the most prevalent," said Axelrod.
Clement, 69-75 in his career, went 9-13 last season in Chicago. The Indians identified him early in the free-agent process and have pushed hard to sign him.
General Manager Mark Shapiro thinks he'd be a solid No. 3 starter following C.C. Sabathia and Jake Westbrook.