The club are currently residing at a training base near Enschede in Holland, and face Dutch second tier side Den Bosch on Tuesday evening.
Mustafi, who was born in Macedonia but has five caps for Switzerland U21 side, made only four league appearances last season, all as a substitute.
"We want to take a right good look at Mustafi during the training camp and he is with us for the week," County boss Derek Adams said in the Daily Record.
"He has another year on his contract at Grasshoppers, so we would probably have to take him on loan.
"The forward area is probably the only one we would need to strengthen."
Adams also confirmed that the Staggies were interested in signing Dundee United defender Brian McLean, and are trying to broker a deal for a player with one year remaining on his Tannadice contract.