The Blues tackle the Gunners on Monday bidding for a victory that could take them top of the Barclays Premier League at Christmas.
Cole, who made a controversial move from Arsenal to Chelsea during Mourinho's first spell as boss, has been out of favour in recent months and is likely to be on the substitutes' bench at best on Monday.
Mourinho said: "I have my opinion, but I keep (it to) myself. It was a free day for them, so I'm not a father, I'm a manager, and I can't control what they do when they are not with me."
Cole played in Tuesday's Capital One Cup loss at Sunderland, when Cesar Azpilicueta was at right-back due to the suspension of Branislav Ivanovic.
With Ivanovic available again at Arsenal, Spain right-back Azpilicueta will revert to left-back, where he has performed well in recent weeks, keeping Cole out of the side.
Mourinho added: "From the beginning Ashley's not playing, (but) today is Friday, the game is Monday. Something can happen in between.
"I play Ivanovic right-back, I play Azpilicueta left-back. I play John Terry and I have to choose between (Gary) Cahill and David Luiz."
Michael Essien is banned after picking up a fifth yellow card of the season at Sunderland and his fellow midfielder Marco van Ginkel (knee) is a long-term absentee.