Arsenal only have a reported £40m transfer budget following their failure to qualify for the Champions League.
The limited warchest follows on from the winter window when Emery revealed Arsenal could only sign players on loan.
Emery has identified a number of positions in which he wants to improve the side such as left-back, centre-back and on the wing.
The club have made offers for players in all of those positions but have been knocked back in their efforts to sign Kieran Tierney, William Saliba and Wilfried Zaha.
According to football.london, the pair will have discussions about transfer budget and policy by the end of the week.
Kroenke resides in Columbia, Missouri, which is not particularly close to any of Arsenal’s tour games in Denver, Los Angeles, Charlotte and Washington DC.
Director Raul Sanllehi is also expected to be privy to meetings and the front office will seek approval from Kroenke to splash more cash.
Arsenal flew out to USA yesterday to kickstart their pre-season and Emery is set to hold talks with Kroenke over a deal.
Emery is aware he can boost his transfer funds by selling players but wants to keep his most valuable assets.
The club have reportedly cleared £410,000 from their weekly wage bill following the departures of Aaron Ramsey, David Ospina, Petr Cech, Danny Welbeck and Stephan Lichsteiner, whose contracts expired.
Emery’s plans for a new centre-back were dented on Thursday afternoon as Laurent Koscielny refused to board the plane to USA.
The Frenchman has one year left on his contract and is angered the club have not allowed him to leave and return to his homeland.