The Blues face Arsene Wenger's side knowing that a victory could move them to the top of the Premier League table at Christmas.
Cole, who controversially left Arsenal to join 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 started at left-back in Tuesday's Capital One Cup loss at Sunderland, when Cesar Azpilicueta was switched to right-back due to the suspension of Branislav Ivanovic.
With Ivanovic available again at Arsenal, Spain right-back Azpilicueta will revert to left-back, 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."
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He attends the Christmas party of a team he publicly mocked/mocks? Lolwut?- mootilated