The gap is there because of interest rate differentials between the two currencies. So short answer to your question is yes this gap will close, but I have a feeling you are really asking if there's a quick, easy profit to be had there, and all you have to do is buy one and sell the other, in which case the answer is no - no such thing as a free lunch. Funding costs for holding your position would pretty much exactly square you up and you wouldnt make any money.
Sorry
GJ