WEDNESDAY and United are set to hold talks to resolve the two clashes in the published fixtures.
It is believed to be the first time that the two Sheffield clubs have been handed home games on the same day by the Football League.
Either the Owls or the Blades are likely to switch to Sunday on one occasion.
The other clash is in midweek so could result in one team playing on Tuesday - the scheduled day - and the other moving to Wednesday.
The League alerted the clubs to the clashes and will leave it to them to come to an arrangement.
Published fixtures for the Championship and League One show Wednesday at home to Huddersfield on Tuesday, September 18, and Brighton on Saturday, February 2, and United at home to Doncaster and Coventry respectively on those dates.
A League spokesman told The Star that sometimes it is impossible to avoid such clashes in the initial fixture list because of the number of areas where teams are ‘paired’ for fixture purposes as they play in close proximity to each other.
He said: “Logistics mean that it is not always possible to avoid two paired teams being given home fixtures - if you move one, it causes a ripple effect on other fixtures. If two teams are given home fixtures on the same day then, after consultations between the clubs and the police it is likely that one of the clubs will play on a Sunday.”
He added that Wednesday and United were aware of the issue and it was up to them to come to an agreement.
There have been instances of the Owls and Blades going ahead with home games on the same day when the Cup has been involved.
For example Wednesday played Aldershot and United faced Torquay in the FA Cup second round on December 3.
But these were relatively small games and each attracted a crowd of only 10,000.
Wednesday alone pulled in 28,000 for last season’s 4-4 thriller against Huddersfield, and it is unthinkable that two well-attended Yorkshire derbies in the League, against Huddersfield and Doncaster, could take place in Sheffield on the same evening.
The Owls’ and Blades’ games against Brighton and Coventry are reasonably high profile.
The issue for September or February would be resolved if a switch is forced by live TV coverage.