The Whites' aim is to get someone in 'early' in the January transfer window, but Kinnear insists quality will be the top priority.
He says Nketiah's return to the Emirates was not a surprise.
"Last week Eddie Nketiah was recalled, as expected by his parent club," said the chief executive.
"While we still firmly believe we could have assisted Eddie's development over the remainder of the season, we respect Arsenal and Eddie's desire for first-team starts, which was always their collective priority."
Anticipating the loss of Nketiah, Leeds started to put the feelers out for a replacement.
Southampton's Che Adams has emerged as a major target, with Billy Sharp another option due to his lack of involvement at Sheffield United in the top flight.
The need for a striker was further highlighted by Leeds' failure to score in yesterday's 2-0 home defeat by Sheffield Wednesday, when the hosts were guilty of wasting good chances - although boss Marcelo Bielsa said the vacancy for a forward could not be linked with the result.
"The process to find Eddie's replacement started as a contingency plan significantly before his departure," said Kinnear.
"Targets were identified and clubs, players and agents have been engaged. Our objective is to move early in the window, but we will not do this at the expense of securing a player of the right calibre."