The Well manager confirmed on Thursday that captain Paul McGinn and left-back Steve Seddon are among several players facing spells out, which also includes influential midfielder Lennon Miller.
Kettlewell, who has already brought in young midfielder Kai Andrews and goalkeeper Archie Mair on loan this window, says the club are “working endlessly” as they aim to “strengthen the group”.
“But I can’t really put a timescale on that,” he added prior to his side’s Scottish Cup trip to St Johnstone on Saturday.
“What I can finish off by saying is the club have been supportive”.
Dundee, who face city rivals Dundee United in their fourth-round tie on Monday, have strengthened their squad this month by acquiring defensive duo Aaron Donnelly and Ilmari Samuels, plus midfielder Cesar Garza.
On further potential transfer business, Dens Park boss Tony Docherty says he is “hoping there might be movement on one other”.
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