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"If I push it, I could go backwards or end up back on medication," he said. "There is also a chance of rejection."
The former Manchester United, Newcastle and Blackburn forward suffered kidney failure in 2015 after contracting an airborne virus.
He has just returned to his role as a United ambassador following surgery.
The 45-year-old is not even allowed to fly to Barcelona for a Manchester United legends game on 30 June.
Cole said: "It is a long road ahead. It is a tough road and different to the battles I have had before.
"It is not like getting a football injury, when you go to the gym and work a bit harder."
His 28-year-old nephew Alexander provided the donor kidney - "a noble job" as Cole described it.
Cole has improved physically and has lost most of the weight he gained through his illness.
And while there is still more work to do, Cole, who will be United's assistant manager for the return legends game against Barcelona at Old Trafford on 2 September, is looking forward to playing if a similar match is staged in 2018.
He said: "I still get very tired but I can do a lot more than I was able to two years ago. If this game is played next year I want to be out there."
Earlier this week, another former Newcastle and England striker, Alan Shearer, told the BBC he felt English clubs were a long way off being able to challenge for the Champions League.
Cole agrees, saying: "From what I have seen in Europe, I am not sure any of the English teams will win it. They are miles apart.
"If you look at Real Madrid, Barcelona or Bayern Munich, a lot of the players people are talking about Premier League clubs paying £50m or £60m for can't get in their teams.
"That tells you where they are at."
Former England striker Andy Cole says he faces a "long road ahead" as he recovers from his recent kidney transplant.