Cook resigned earlier this year after 59 matches and four and a half years at the helm, with Joe Root swiftly promoted to fill his shoes.
Root's vice-captain Ben Stokes, Jos Buttler and Stuart Broad were also vetted for the job but Anderson, the country's record wicket-taker and a veteran of 122 Tests, was not considered or asked to interview.
At 34 and with injuries increasingly taking their toll, the vacancy may have come a little late for the Lancashire seamer but he would still have welcomed being part of the conversation.
"It would have been nice to have been considered for it but whether I would have taken it or not, I am not sure," he said.
"Thinking about it from a personal point of view I would have seriously thought about it. But if I was on the outside looking in I would have thought 'is this actually where the team needs to go, with a 34-year-old as captain?'
"I don't know how long I am going to be able to keep going for and in the grander scheme of things it makes sense for a younger guy to do it."
While Anderson is pragmatic about his own claims on the top job, he is also happy to fight the corner for fast bowlers at large.
Captaincy has become almost the sole preserve of the top order, with only a smattering of names bucking the trend globally in the past 30 years and Bob Willis the last specialist seamer to lead England's Test XI in 1984.
In recent memory only Broad, who grew up as a batsman, has been treated as officer class, serving as Twenty20 captain between 2012 and 2014.
"I don't know why that is," said Anderson.
"Bowlers do tend to get injured, I suppose, and that might be why Stuart Broad didn't get asked this time. There are more injury risks but I am all for bowlers being captain
"Most of the fast bowling captains I have played with or against have been pretty successful - Glen Chapple here at Lancashire won the (County) Championship - so I don't know why more fast bowlers aren't given the opportunity to do it.
"I think they would do a good job and are suited to it."
As it stands Root is the man to lead England into the next phase of their development, with series against South Africa and West Indies this summer and a winter Ashes tour on the horizon. And the Yorkshireman will have nothing but support from his strike bowler, who brings considerable tactical insight as well as the small matter of 467 Test scalps.
"I see myself as a leader within the group, I don't think that changes, and I still think like a captain on the field," he said.
"I still try and help out where I can. For me, my mindset never changes. I'm always thinking about ways to help the team if I'm captain or not.
"It's nice for Joe that if everyone is fit for the first Test we will hopefully have me and Stuart Broad opening the bowling. For a young captain to have experienced guys like that would be really helpful to him and his growth in that role."
