In March, Mosimane declared his admiration for City talisman Lebogang Manyama.
Citizens chairman John Comitis, however, responded by insisting Manyama is not for sale on the local market.
Tinkler and Comitis have since jointly expressed their unhappiness with Mosimane's advances.
“Pitso talks too much,” said Tinkler. “Pitso should rather go through the proper channels than through the media and also through the players if interested in our players.”
The former Bafana Bafana midfielder is adamant City will keep hold of Manyama and fellow KICK OFF Footballer of the Season nominee Aubrey Ngoma.
“We have a very ambitious club owner in John Comitis who doesn’t want to lose his best players. Lebo is not for sale, Aubrey is not for sale.
“Ajax was all about development and moving players on. Cape Town City is not about that. Cape Town City is about wanting to compete and win trophies.
"We know the areas we need to strengthen so that we can be more competitive again next season.”
Meanwhile, Comitis plans to release a statement regarding the issue.
“I will make comments tomorrow in the media regarding Pitso and his approach to players,” Comitis told KickOff.com.
“I think it's out of order. We have no problem with people showing interest in our players, we accept that. We know that we have good players that other clubs would want.
"There is procedure and a process to do. So you need to do it in a professional manner, not in a way to distabilise another club, especially if you are in a title race with the other team.
"I am not happy about that but I will make a proper statement.”