Soriano was pulled from Thursday's Cubs lineup against the D-backs at the request of president of baseball operations Theo Epstein, and appears to be headed to the Yankees.
Physically, Sveum said he'll mix and match in the outfield, using rookie Junior Lake as well as Cole Gillespie in left field. Brian Bogusevic, on the disabled list with a strained left hamstring, could return in early August.
The Cubs may decide to add a pitcher when they make a roster move rather than an outfielder because the bullpen has been overworked, and they have a doubleheader coming up on Tuesday.
Soriano, 37, was one of the few veterans in the clubhouse.
"You have [Kevin] Gregg, [David] DeJesus, and other than that, it's a lot of young guys," Sveum said. "With the addition of Lake, now we're getting pretty young."
The Cubs were busy at the Trade Deadline last year, and this season, have made six deals before July 31. The only players who were on the Chicago roster when Jim Hendry was the general manager are Starlin Castro, Darwin Barney, Welington Castillo and Jeff Samardzija.
The Cubs may find another left fielder, but can't replace Soriano's professionalism.
"You don't replace that," Sveum said. "Hopefully, down the road you do. You don't have a Band-aid right now to replace that kind of guy in your clubhouse."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.