Anthony, 30, is expected to re-sign with the Knicks, but the NBA franchise are still waiting for confirmation.
Jackson expects a positive outcome despite not hearing from Anthony since their conversation in Los Angeles on July 3.
Asked on Thursday if they had spoken, Jackson said: "I text him a couple of times, but no (reply).
"I felt really good about my conversation with Carmelo (on July 3). We really struck a chord.
"The two of us, I think, feel really passionately about what we're trying to get accomplished.
"It's his ability to stay, be patient, lead and watch us develop a winner. There's no instantaneous winner that we think is going to happen to the Knicks right now, but we're going to be a lot better."
Jackson said the Knicks had back-up plans should Anthony decide to leave, with the Chicago Bulls and the Los Angeles Lakers his most likely destinations in the unlikely case he departs.