I am a final year PhD student and given the competition and burden of finding a PostDoc position, I want to try to apply to some positions early on. At this stage I am satisfied with the group and would like to continue working here, unless, I get accepted at Harvard or MIT.
The constraints: (1) I want to continue in Academia and it is clear to me that research experience abroad (I am not in USA) is a must. (2) I did not have any conversation about the possibility of having a PostDoc position with my supervisor. I think it is too early for her to know if she will have the money in one year. So I did not ask, I focus on my performance. (3) The application for MIT is open and ends in about a month. It would be a dream come true if I can go there. (4) I would like to be a citizen of the country I am living in (in Europe) and by doing my PostDoc here I could achieve that. This conflicts with (3) and (1).
Given the above points, I would like to at least try to apply to MIT and see if they accept or reject, you never know until you try. But I prefer to not have my current supervisor think that my application at MIT (I need her L.O.R) means I am not interested in working here as PostDoc anymore and therefore not look for funds for me (which is significant work).