Alexander, 53, collapsed after returning from a League Two game at Notts County on Tuesday night.
Like in 2003, when Alexander - the first black man to be given a permanent manager's job in the United Kingdom - was rushed to hospital with a brain aneurysm after attending a reserve fixture, there had been no warning.
Alexander and Laws crossed paths many times in Lincolnshire, when Laws was in charge at Glanford Park and Alexander was in charge of Lincoln City.
The League Two play-off semi-finals in 2002/03 were a highlight, with Alexander’s Imps triumphing 6-3 on aggregate to reach the play-off final.
“He had a bad time at Lincoln but overcame everything and we had some right ding-dongs when he was there and I was at Scunthorpe because that was our local derby,” said Laws, now in charge of the Premier League side Burnley.
"One thing that has been very solid has been our relationship all the way through, which was fantastic.
"He broke the mould as one of the first black managers to have success and some time in football whereas a lot of managers particularly in that era were very short-lived. He is going to be a sad loss to football."
Macclesfield’s League Two game against Hereford United will go ahead despite Alexander’s death.