Kenney is the Cubs’ president of baseball operations, so consider that an official acknowledgement of their plans.
The 2017 All-Star Game will be in Miami, and in 2018 the Nationals will host. The 2019 Midsummer Classic hasn’t been awarded yet, but presumably it will go to an AL team (the league doesn’t strictly alternate AL-NL All-Star Game hosts anymore, but it’s hard to imagine such a long run of NL hosts). By 2020, those sprawling Wrigley renovations should be complete, and the ballpark should be up to MLB‘s specs for hosting. In the past, MLB has “rewarded” teams for securing public financing for new or renovated ballparks, but in the Cubs’ case their Wrigley renovations are mostly financed with private capital. Perhaps, though, the “get tax dollars, get the All-Star Game” phenomenon is mostly a Bud Selig-era relic.
In any event, the Cubs haven’t hosted an All-Star Game since 1990, so it would indeed be their “turn” around 2020. The crosstown White Sox last hosted the event in 2003.