The Germany international is reportedly set to sign for the Blues in a deal worth £90million (€100m).
Havertz would become the seventh signing for Chelsea during a transfer window of significant investment, with Timo Werner, Hakim Ziyech, Ben Chilwell, Thiago Silva, Malang Sarr and Xavier Mbuyamba also having moved to Stamford Bridge.
Bosz appears confident that neither Havertz nor Kevin Volland, who is expected to join Monaco, will be around for much longer.
Speaking to reporters on Monday, he said: "Unfortunately, our squad has not yet been determined.
"I don't expect Kevin Volland or Kai Havertz will train with us again. It's possible that other players will also leave.
"We definitely have to bring in players, too. Normally a pre-season takes six weeks, so it's an advantage that I'm not new here.
"It would be great for coaches if the squad were completely ready by the start of training, but that's almost never the case these days. The coronavirus [pandemic] has shifted things a lot. That makes it complicated.
"As a coach, it's my responsibility to deal with it."
Havertz scored 19 goals in all competitions last season as Leverkusen finished fifth in the Bundesliga, reached the quarter-finals of the Europa League and the final of the DFB-Pokal, where they lost to Bayern Munich.