Director of sports Stefan Alven says a few details remain to be worked out before the contract can be signed.
The 19-year-old was training with Djurgarden on Tuesday after spending a week in New York, following a two-week trial with the Stockholm club.
Agbossoumonde said he was happy to be back and "to finally have a team."
In December, Agbossoumonde was cited as the top young male player of 2010 by the U.S. Soccer Federation. He has previously been with Miami FC and Portuguese clubs Sporting Braga and Estoril. He made his debut for the U.S. national team in November and is on the American under-20 team.
Djurgarden has reserved an option to purchase Agbossoumonde when the loan expires.