Sources claim that Price is tiring of the Argentinian model acting like "a spoilt teenager" and their lack of communication, while he is said to have requested they take some "time apart".
"Leo is tired of the arguments between him and Katie, and thinks they both need some space and time apart if they're going to make their relationship work," an insider told Closer.
"Some days, they barely seem to talk and the atmosphere can be terrible."
Another added: "[Katie has] told pals she's tired of the language barrier and thinks that Leo can sometimes act like a spoilt teenager.
"But although she's dreading being single again, she's hoping she won't be on her own for very long."
A representative for Price has however denied claims by the publication that tension between the couple is down to Penna's planned move to Miami.
Price stated back in July that she will not marry Penna, who she has dated on-and-off since February 2011, unless he agrees to a pre-nup.