Reports had linked PSG with a renewed interest in the former England captain, 37, who announced on Monday night that he will be leaving Los Angeles Galaxy following the MLS Cup final in December.
PSG targeted Beckham last January but he chose to remain in MLS rather than return to Europe for family reasons.
Now the French side, who take on Dynamo Kiev in the Champions League on Wednesday night, say they will not be amongst the group of clubs that will inevitably attempt to sign the former Manchester United, Real Madrid and AC Milan midfielder.
"We did not offer, good luck to him," Ancelotti said.
When asked why the club were not considering a move for the midfielder, Ancelotti replied: "Because our market is over."
Beckham has been most strongly linked with a move to Australia as a number of A-League clubs have already expressed an interest in signing him.
He says he has plenty of "exciting opportunities" to consider once his six-year playing career with the LA Galaxy ends.
Ruling out retirement, former England captain Beckham said he still has one more challenge to face on the field but will not decide on his next move until the end of this year.
"I still feel I have something left in me as a player," the former Manchester United and Real Madrid mid-fielder told reporters after a Galaxy practice session at the Home Depot Center on Tuesday.
"I still feel like I have one more challenge in me as a player, even at 37 years old. I feel I still can play at a high level. Where that will be yet, I haven't decided.
"I have some exciting opportunities on the table but right now my focus is on the final. Once that's out of the way, we have a tour to deal with and then it's Christmas, which we always spend in London. I will make a decision then."
Last week, Beckham's management denied he had plans to move to Australia's A-League though his decision to leave the Galaxy has prompted huge speculation over his next destination, with a return to England one of the options floated.
Asked if he could be more specific about his next move, Beckham replied: "No, because right now my focus is on the final and I haven't made a decision on that yet.
"There are options and I am very lucky at my age to have options. My decision will be made around December or in the New Year but right now I can't even comment on it."
Beckham has spent six seasons with the Galaxy and in January he signed a new two-year contract after his team won the MLS title. However that deal included an option on the second year and, after careful consideration, he decided to leave the club.
He will play his final game on December 1 in the MLS Cup final against Houston Dynamo at the Galaxy's Home Depot Center.
"I came to the decision (to leave the Galaxy) solely because I felt I had achieved everything I wanted to achieve with the Galaxy, on the field and off the field," said Beckham, who earned 115 caps for England.
"On the field, to have played in three finals, by the time next Saturday comes around, in six years, and to have been able to lift the championship last year in our own stadium, I felt that I had achieved everything I wanted to do.
"Now that we have reached the MLS Cup final, that it is going to be in our stadium again in front of our own fans, it just felt it was the right time (to bow out)."
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