The Sun says Kroenke has flown in from the US with the specific purpose to map out their summer market plans.
Kroenke will attend Sunday's Carabao Cup final against Manchester City at Wembley before entering meetings with manager Mikel Arteta and sporting director Andrea Berta during next week's international break.
A raft of summer targets are being discussed, including Newcastle trio Tino Livramento, Sandro Tonali and Anthony Gordon.
Atletico Madrid striker Julian Alvarez and RB Leipzig defender Castello Lukeba are also on Arsenal's radar, along with Inter Milan centre-forward Francesco Pio Esposito.
Arsenal will need to sell to avoid Profit & Sustainability concerns, with the likes of Leandro Trossard, Gabriel Martinelli, Ben White, Gabriel Jesus and even Martin Odegaard all potentially available this summer.