Cole has spent a season on loan with Ligue 1 side Lille this term, with the French club thought to be open to taking the former Chelsea man back for another 12 months.
But the 30-year-old, who has been linked with a return to Upton Park where he spent five years, admits he would still relish the chance to play at Anfield again.
"When I signed for Liverpool, it startled me a bit," said Cole.
"I don't know if I felt the pressure but the city is so in love with football. It's a religion. If I go back, I will be more prepared for it this time.
"I can see why people say (joining Liverpool) is a culture shock. It is a small place but it has this great buzz.
"How can there not be in a city that has produced five Prime Ministers and The Beatles? The people are so sharp, quite a bit like Londoners really.
"There is still a part of me that would really love to make it work there and I don't want to have a bad spell at Anfield on my CV. But it is out of my hands now.
"At the minute I can't rule anything in or out. We have got to speak to Liverpool and see what happens there."
He added: "I haven't played for England for two years. I know there is a new manager but I was never contacted. I heard there were strange things going on with the odds of me being cut to make the squad and that made me think "maybe".
"But I have got my eyes on the Olympics now. I am in the mix and it would be amazing to play in that but, again, it is out of my hands.
"We will just have to wait and see what happens. Whatever is the case, it has been a great year and it has been a great season. I am delighted with how things have gone."
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