Van Persie netted 58 goals during a three-year spell with United and on Thursday night, he makes his return to the North-West in a Fenerbahce shirt for the Europa League clash between the two teams.
The Dutch forward has only scored once in all competitions this season but Shaw insists that he and his teammates cannot afford to give Van Persie any openings in the final third.
The 21-year-old told reporters: "He is definitely a threat. We know what his qualities are but with quality like that even if you know what they might do it is very hard to stop.
"I was able to see how good he was in training and games."
Fenerbahce head into the fixture at the top of Group A but United sit just one point behind them heading into Matchday Three.