Cowan was dropped from Saturday's Off The Ball show on Radio Scotland, which he co-presents with Stuart Cosgrove, and is due to meet BBC Scotland's Commissioning Editor Ewan Angus to discuss his future after the comments in his Daily Record column came under fire.
He used his column yesterday to offer an apology for his remarks and has said he plans to make a donation to Scottish Women's Football.
Describing how the episode had "not been my finest hour and a half", he wrote: "The reaction to Saturday's piece on women's football has been quite incredible but I can assure you I meant it tongue-in-cheek.
"Hands up it was a spectacular OG and I want to apologise to anyone who was offended. Particularly Scottish Women's Football.
"In 15 years as a Daily Record columnist it has never been my objective to deliberately upset readers - that's a totally pointless exercise - and I've only tried to have a laugh, a joke and a carry-on.
"I've never expected anyone to take my column too seriously and I suppose my patter's a bit like a bride on her wedding day - something old, something new, something borrowed and, yes, something blue."
The presenter's comments came after Scotland's women football team made it two wins from two in their 2015 World Cup qualifying campaign, scoring 14 goals in the process and conceding only two.
The Scots last week beat Bosnia 7-0 and have already defeated the Faroe Islands 7-2.
Cowan said he hoped they go on to qualify for the tournament as "apart from anything else, I will be six feet under by the time the men have done it."
He added: "As you can imagine, I've already received several offers to attend a few training sessions with women's teams but I think I'll pass as I now appreciate how much it would please some people if I suffered a massive heart attack.
"I've often said I wouldn't open the curtains if a women's football match was being played in my back garden. From now on, the curtains will probably still remain shut. But so, I promise, will my mouth."
The Record took a circumspect view on Cowan's writing, suggesting his views "should be taken with a pinch of salt". However, his suspension suggests the BBC is taking a more serious stance.
In his original column, Cowan described some women footballers as "blokes" and wrote of the international at Motherwell's Fir Park ground: "Face it, folks, nobody cares about women's football. There was barely a thousand there ... and I guess putting the girlies head-to-head with Emmerdale and EastEnders was a bit daft."
Maureen McGonigle, executive administrator for Scottish Women's Football, said the comments were very narrow-minded.
A spokesman for BBC Scotland said the meeting between Cowan and Ewan Angus was yet to take place and that nothing had been decided yet.
The BBC was caught up in a sexism and sport row earlier this year when John Inverdale was criticised over remarks he made on air about Wimbledon women's champion Marion Bartoli
More than 1000 people, including Westminster Culture Secretary Maria Miller, complained after the 55-year-old said the French ace was "never going to be a looker" following her victory over Germany's Sabine Lisicki.
However, BBC director General Lord Hall decided not to sack the presenter after both he and the BBC apologised for the remark.