The Premier League side completed a deal for the USA international in January but he won’t arrive at Stamford Bridge until the summer, and former England and Crystal Palace manager Allardyce has questioned the Blues’ approach.
"I am staggered and shocked," he told Sky Sports News.
"What if he does an ACL [anterior cruciate ligament] over there?
"You invest that much money and then you have the settling in period... next season, who knows, he might come in and struggle."
The 20-year-old winger has scored three goals in 19 appearances in all competitions for Bundesliga leaders Dortmund this season.
'People will remember us because we got to No.1 in the world rankings and achieved great things - but our biggest regret is that we didn’t win anything': Ex-Everton star Kevin Mirallas opens up on 'honour' of being part of nation's golden generation
‘I’m sure we’d have finished in the top four or five if he hadn’t joined Chelsea in January. Him leaving damaged the team, but we couldn’t stand in his way’: Alan Curbishley reflects on failed Champions League dream after selling key player
