The terms of the offer for the veteran power forward are undisclosed at this point.
The Knicks have been after Brand since the start of free agency. Brand, 34, provides scoring and rebounding, which the team needs. Brand is not only a solid rotation player -- he is fine with coming off the bench -- but insurance, as well, considering Amar'e Stoudemire's recent injury history.
Several other teams have expressed interest in Brand, according to the source. Brand also remains "very interested" in returning to the Mavs, he said in a text message to ESPNDallas.com's Tim MacMahon. Dallas contacted Brand in the opening minutes of free agency to touch base.
Brand is attracted to the Knicks because of their winning culture and first-class organization, the source said. In addition, the team is close to his hometown -- Peekskill, N.Y. -- and his mother, Daisy, still lives nearby. Quality of life is also important to him as he decides on his next team, the source said.
Brand has averaged 17.4 points, 9.1 rebounds and 1.8 blocks in his 14-year career. Last season in Dallas, he averaged 7.2 points, 6.0 rebounds and 1.3 blocks in 21 minutes per game.
If the Knicks sign Brand, they might not consider re-signing power forward Kenyon Martin. They also need a point guard and small forward. A league source told ESPNNewYork.com on Tuesday that "both [point guard] Nate Robinson and [small forward] Matt Barnes have notified the Knicks of their interest. They're waiting to see where the Knicks are."
Up next on the Knicks' immediate priority list is re-signing J.R. Smith and then potentially splitting up their mini midlevel exception of $3.18 million to sign Pablo Prigioni and Chris Copeland. While Prigioni is likely deciding between the Knicks and returning to Spain, where he lives in the offseason and has played professionally for many years, Copeland already has received several offers from different teams.
Information from ESPNDallas.com's Tim MacMahon was used in this report.