"We can't be responsible for comments by managers, club presidents, lawyers, players," Arena said. "We did things properly, ethically and we're going to hold up the loan agreement."
After Beckham scored in AC Milan's 4-1 win at Bologna on Sunday, AC Milan coach Carlo Ancelotti said he wanted the Englishman to stay with the club: "He knows our desire, if he goes it will be a disappointment because of the contribution he is giving [in terms of] quality and balance. If he leaves, that will sadden us because of the help he's giving in terms of quality of play and balance."
For his part, Beckham said, "I feel very good here. I arrived in a team that wanted me for years and I play for exceptional fans. I'll stay here until March and then we'll see."
Arena, who is also threatened with the loss of leading scorer Landon Donovan, who has repeatedly said he wants his loan with Bayern Munich, for which he has scored four goals in five friendlies, to turn into a transfer.
"We've got two players out on loan agreements and those loans end March 8," Arena said. "We set conditions and we've lived up to our part of the loan agreements."
Arena also refuted British tabloid rumors that the Galaxy is after England star Michael Owen, currently captain of Newcastle United.
"I can promise you we have had zero contact with him, so there's probably zero percent accuracy in that report," said Arena.