Since you are a US citizen you can petition for your parents. The question is whether when they came into the US if they came with a visa or without a visa or if any other previous petition has been filed on their behalf before 2001.
If they came with a visa or lawful entry, they will be able to adjust their status here in the US. If not, they will have to leave the US and it becomes very complicated, especially if they have been here for so long.
You can petition your parents, but whether they will get the green card depends on a number of factors:
1) If they entered the US legally and can prove it, then they should have no problem.
2) If they did not enter the US legally, then they will have to qualify for 245(i) or wait for a change in the law in order to be able to get the green card in the US. To qualify for 245(i) they must have been in the US on December 21, 2000 AND have had a petition filed for them on or before April 30, 2001. If they do not meet both of these conditions, they do not qualify for 245(i).
3) If they do not qualify for 245(i), then they can only get the green card abroad. But, if they leave the US, they will not be able to come back for ten years, unless they have obtained a waiver of that bar.