Arsenal claimed a 1-0 win over title rivals City thanks to a late goal by Gabriel Martinelli and Gunners set piece coach Nicolas Jover, who used to work at City, sought out Walker after the final whistle.
The Sun reports that Walker reacted angrily because Jover refused to shake hands with his former friends at City after both Premier League matches against Arsenal last season.
The post-match scenes saw Walker square up to Jover near the tunnel.
Haaland then waded in to keep the pair apart before other players and backroom staff also got involved.
The report adds that Jover, who worked under Pep Guardiola at the Etihad Stadium for two years, stood with his hands behind his back after City's victories over Arsenal in February and April, results which proved to be key in deciding where the title ended up.
READ MORE ON ARSENAL
Guardiola speaks on scuffle involving Man City duo as footage shows start of incident
Raya faith, Haaland problem and history made - Things learnt from Arsenal's win over City
It's said Jover made it clear he wouldn't shake hands with anyone from City then but wanted to do so after Arsenal's win - their first against City in the league in 12 attempts.
The 41-year-old is understood to have left City on good terms in December 2021, meaning his reaction at the end of the two matches last season may have come as a surprise to those associated with the Premier League champions.
The Football Association will not be taking any action against Walker, Haaland or Jover over the incident having reviewed footage on Monday.
Arsenal boss Mikel Arteta says he didn't see what sparked the incident, while City manager Pep Guardiola get his cards close to his chest on its causes.
Most read in Football
Rooney to Birmingham, Saka ruled out of England clashes, Beckham may return to Man United
Saka sent back to Arsenal after joining England teammates at St George's Park amid injury
Fans love Roberto De Zerbi's classy gesture after Brighton draw with Liverpool
David Beckham lined up for Man United role if Qatari bid is successful
"I know what happened, but I don't want to say anything," Guardiola said. "They [Arsenal] know it."