Kosovo, who play their first competitive international on Monday when they visit Finland in a World Cup qualifier, were accepted as members of FIFA and European football's governing body UEFA in May despite fierce opposition from Serbia.
FIFA told Reuters that it had received a "series of requests for change of associations from the Football Federation of Kosovo.
"The various applications are currently pending and being investigated. As a result we are not in a position to further comment on them, nor to give an estimation of the time line."
The Swiss federation (SFV) said its players with Kosovar roots had been put in "a very difficult situation" and criticised FIFA for failing to clarify the situation. Albania also have players with Kosovar roots.
Kosovo, who declared independence from Serbia in 2008, said on Wednesday they had made requests for nine players to switch national teams, without identifying them.
FIFA does not ordinarily allow players to switch national teams once they have represented one country in a competitive international.
However, the statement said it was not clear whether these rules were applicable if players wanted to change to a team that had not previously been a FIFA member.
BUNJAKU SWITCH
"The specific circumstances of the matter at hand concerning the admission of a new member to FIFA and players potentially eligible to play for it appear not to be conclusively governed (by the statutes)," added football's ruling body.
It said FIFA's players' status committee were considering the requests "while taking into consideration all relevant and specific facts and circumstances of the matter".
FIFA has already allowed Alberto Bunjaku, who made a brief appearance for Switzerland at the 2010 World Cup, to play for Kosovo.
Finland's Kosovo-born midfielder Perparim Hetemaj has said he will not play in Monday's match.
The Swiss federation complained in a statement that "the current situation suffers from the lack of clarity in regulations.
"The SFV wants this situation to end as soon as possible. Unfortunately UEFA and FIFA have not responded to these approaches.
"The SFV regrets the priority of the Kosovar directors has been in trying to recruit players for the next World Cup qualifiers instead of consolidating the foundations of their federation.
"This frantic search has put the players involved and sometimes their families in a very difficult situation. The SFV strongly condemns this slanderous and disrespectful way of proceeding."
(Editing by Tony Jimenez)
