The three veteran midfielders are struggling for game time and Arsene Wenger is said to be undecided on their future.
The three midfielders’ contracts all run out at the end of this season, and the club are yet to offer them new deals.
So far no final decision has been made on whether they will be offered fresh terms, but it is believed that the club are preparing for life without their more experienced performers, according to the London Evening Standard report.
Of the three, Rosicky is the most likely to leave as he turned 35 last month and is yet to feature this season, with him set to be missing until Christmas after undergoing knee surgery.
The Czech Republic international was reportedly close to leaving the club last summer, only for Arsene Wenger to have a late change of heart and extend his contract by a year.
The French boss is reportedly concerned about his ability to perform at the highest level on a consistent basis, a fear he shares with fellow midfielder Mathieu Flamini.
The Frenchman was another linked with an exit in the summer, but failed to move on, and his recent poor performance in the loss to Sheffield Wednesday has the club considering his future, according to The Standard.
Arteta seems the most likely to remain, as he is still club captain and his professionalism in the dressing room is highly valued by Wenger.
However, he has struggled for game time this season, having started just two games, with midfielders Santi Cazorla and Francis Coquelin forming a strong central partnership and limiting his opportunities.
That could see him leave alongside the other two, although at present, any decision remains firmly with Wenger and their ability to find suitable replacement in the summer transfer window.