But he also does not plan to select the England left-back for Chelsea's top-of-the-table trip to the Emirates Stadium.
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."
There is a bitter history between Arsenal and Chelsea relating to Cole.
Mourinho and Chelsea were fined for 'tapping up' the England defender before recruiting Cole in August 2006 in a swap deal which saw the Blues pay the Gunners £5million with William Gallas going in the opposite direction.
Cole has started two matches since the November 2 loss at Newcastle - the Champions League win over Steaua Bucharest and the Sunderland defeat - but is still to return to Premier League action, with Azpilicueta preferred.
On Monday, Cole will be "on the bench or at home", Mourinho confirmed.
The Chelsea boss has defended Cole's professionalism in recent weeks, despite keeping him out of the side, and declined to question it on Friday.
Mourinho said: "Not even to Ashley Cole have I given my opinion, because I don't have to.
"It was his free day, it was his free night. The next morning we didn't train, we trained only in the afternoon.
"I have no right to make any kind of comment."
Mourinho has promised to select his strongest XI against Arsenal for Chelsea's seventh of nine December matches, meaning Cole no longer is part of that line-up.
"Of course I'm going to choose the team that I think is the best team to play that game," Mourinho added.
"I'm not playing against Arsenal thinking that two days later I have to play against Swansea (on Boxing Day).
"I'm going to play that game as it was the only game. Nothing else."
Chelsea have already won at the Emirates Stadium this season, claiming a 2-0 win in the Capital One Cup two days after beating Manchester City in the Premier League.
Azpilicueta was out of favour at that point and made just his third start of the season as Mourinho made 10 changes, but has now seized his chance, initially after Cole suffered a niggling rib injury.
Mourinho places no significance on the League Cup win ahead of this season's first Premier League meeting with the Gunners.
"Different competitions, different motivations, different responsibilities, different players in some cases," Mourinho added.
"Still Arsenal, still Chelsea, still a London derby, plus the fact that the first is playing the third, or the second, whatever you prefer.
"(It is a) big match for sure. It's a pity that it's not tomorrow because I'm waiting for the game and I'm ready to play the game and I want very much to play the game."
Wenger may not be so keen to play, given in nine meetings with Mourinho, the Frenchman is yet to taste victory.
Mourinho's Chelsea have won five and drawn four times in a duel which dates back over nine years.
The Portuguese played down the personal record, insisting the sequence is merely because his side has played better on each occasion.
"It's not me against Wenger," Mourinho added.
"It's my Chelsea against his Arsenal. And that (the record) doesn't play Monday. It has no influence. That stat, for the game of Monday, means nothing.
"I just feel that we played better, we deserved more and we won these matches.
"In my time I remember just one game where we were close to losing, which was a game at home where (Michael) Essien scored the equalising goal in the last part of the game (in the December 2006 Premier League draw).
"After that, even at the Emirates, playing with 10 men for 75 minutes we played a fantastic match and we drew 1-1 (in May 2007).
"My memories are that against them we played very good matches. As a consequence of that we got good results."
Following the Arsenal match, Chelsea play Swansea on Boxing Day and Liverpool on December 29, before the New Year's Day trip to Southampton.
Mourinho enjoys the busy festive programme and has two Christmas wishes.
"I want to win on the 23 and the 26," Mourinho added.