Koeman is said to have had the Arsenal striker in the building at Everton.
In an interview in his native Netherlands, Koeman claimed to have been left hamstrung by Giroud's decision to remain in London, having had the Arsenal striker in his office at one stage during the summer transfer window, while also blaming an unfavourable run of fixtures for Everton's poor form, which prompted his sacking on Monday.
And after previously suggesting that Koeman only had himself to blame for Everton's decision, Ball, the former Toffees left-back, was quick to poke holes in the Dutchman's latest excuse.
"What about last seasons 2 wins in 12?Media forgetting about," Ball posted on Twitter.
"EXCUSES MY AR**
"I wonder was it his personality that Giroud saw & walked out!"
What about last seasons 2 wins in 12?Media forgetting about.— Michael Ball (@bally03) 25 October 2017
EXCUSES MY AR**
I wonder was it his personality that Giroud saw & walked out! https://t.co/l5YVpymccD
Following Giroud's snub, Everton, who sold last season's top scorer Romelu Lukaku to Manchester United in July, were unable to recruit a natural number 9, leaving Dominic Calvert-Lewin, Wayne Rooney, Sandro Ramirez and Oumar Niasse to share responsibilities up front.
Meanwhile, Giroud has found himself down the pecking order at Arsenal, after the Gunners signed another French striker, Alexandre Lacazette, for a club record fee from Lyon.