Ibrahimovic scored four goals to beat England last Wednesday, prompting praise from all quarters.
Reid said that he tried to sign the 31-year-old when he was at Ajax, after previously failing with a bid when the forward was at Malmo.
"When he was at Ajax, I went to Amsterdam and offered £7m for him," Reid told the Daily Star. "It was the second time I tried to take him to Sunderland.
"We were also in for him when he was at Malmo.
"Imagine what a signing he would have been, everywhere he goes his teams wins the league."