"If other people want our players, we're prepared to match them and that's what my owners say," Tinkler told The Sowetan.
In March, Mosimane publicly stated that they would like to sign City captain and striker Lebogang Manyama.
"Pitso talks too much. He needs to go through the proper channels instead of through the media and through the players," he said.
"There have to be plans to beef up the squad for next season because we're not here just to make up the numbers," he continued.
"We've proved that this year and we've got a very ambitious club owner in John Comitis who doesn't want to lose his players," Tinkler added.
The Citizens, who are having a great season, are keen to keep their key players.
"Aubrey Ngoma is not for sale, Lebogang is not for sale. Ajax was all about development and moving players on," he stressed.
"We're not about that business. We want to win trophies," Tinkler concluded.