Although I am not a Fannie Mae Listing Broker, I would speculate that the answer is "NO"
I have never seen or dealt with an example where an REO company accepted an offer with a contingency to sell another home attached to it.
I have been involved in several REO transactions.
I agree with both answers.....HIGHLY UNLIKELY. The addendum you need to sign should state that fact. However, Tony has a point. If this property has been unsold for several months they may accept. Hey....all you can do is try. Submit an offer and see if it flies.
I have never seen Fannie Mae or any other REO seller accept a sales contract with such a contingency. The only acceptable contingency would be for appraisal or financing. REO sellers expect to close in 30-45 days on average.