Arsenal said in a statement that Kroenke, owner of the U.S. Colorado Rapids soccer team and a member of the Arsenal board, now held 20.5 percent. Fiszman now owns just over 16 percent of the total issued shared capital.
"I am … delighted that (Kroenke) has shown this desire to deepen his ties with Arsenal," Fiszman said in a statement. "I will of course continue to work for Arsenal with the best interests of the club at heart and have no intention of selling any more of my shareholding."
Fiszman, who was heavily involved in developing Arsenal’s Emirates Stadium, told the club’s Web site he was still fully committed to Arsenal and saw Kroenke’s increasing involvement as a positive development.
Arsenal, drawn against Villarreal in the next stage of the Champions League, have been at the centre of takeover speculation after Kroenke and then Russian billionaire Alisher Usmanov started building up stakes.
Most Arsenal board members had jointly agreed not to sell their stakes for a set period in an effort to stave off a takeover. Fiszman said the other members had agreed to the sale however.
"Stan Kroenke has proved to be a valuable member of the board and I am pleased that he has demonstrated further commitment to the club by adding to his shareholding," Chairman Peter Hill-Wood said in a statement.
"Danny Fiszman remains a driving influence on the board and is fully committed to the club’s long term future."
Kroenke has previously said he is not interested in pursuing a full buyout. Usmanov is the largest shareholder with around 25 percent.