The People says City are planning a £50million double bid for the midfield pair.
Director of football Txiki Begiristain flew to Dortmund to run the rule over the players as they helped to see off Shakhtar Donetsk in the Champions League.
But last season's Bundesliga champions are reluctant to sell - and neither player is in a rush to move.
Striker Reus, 23, is under contract for a further four years, while 22-year-old playmaker Gundogan has a deal through to 2015.
A top German source revealed: "Dortmund do not have to sell, and the players would not necessarily regard it as a step up to join Manchester City.
"They are playing in front of 80,000 fans in Germany and are making more progress in the Champions League so they are not looking to leave."