The Swedish champions and the Serbian champions are at half-time in a two-legged Champions League second qualifying round tie with the prize for the victors a third round tie against us.
The first leg finished in Belgrade finished 1-1, giving the Swedish side a potentially vital away goals advantage.
"When I heard the result from Belgrade, I was more than a trifle surprised and I suppose deep down it actually pleased me," said Sir Bobby.
"Before last night, I thought Partizan would be favourites and that's who we would be meeting.
"But now that Djurgarden have picked up a draw in Belgrade, they will be fancying their chances of finishing the job off in Sweden.
"Perhaps that would be best for us, bearing in mind the technical ability teams from the former Yugoslavia have always had.
"But if we do have to go to Stockholm, we know that it will be just as tough against the Swedish side, for if Partizan Belgrade have the technical ability, then the Swedes have really improved their football in recent seasons.
"And, as we saw in the World Cup against England in Japan last year, the Swedish national team is a difficult one to beat and I am sure that is also the case with their club sides.
"For as long as I can remember, the Swedes have been good athletes and they are strong and very fit."