The German international, who was born in Poland, played against the Claret and Blue in last season's UEFA Cup group stages as Hamburg claimed a comfortable 3-1 home victory.
And with his then manager Martin Jol having recently left for Ajax, Trochowski is said to be considering his future with a host of clubs vying for his signature.
The 25 year old would provide much needed competition for current Villa wingers Ashley Young and James Milner, who were forced to play in almost every game of the last campaign due to a lack of reinforcements.
If Martin O'Neill does miss out on former Bayern Munich man Trochowski and Spurs are successful in their bid then David Bentley could come to Villa Park from White Hart Lane in a cut price deal.
But tricky wide man Trochowski is O'Neill's No.1 target.