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”.
Ronnie Kelly had a goal chalked off as Pickering dominated the opening half-hour, but they were ultimately made to pay for not taking their chances.
The top stories and transfer rumours from Monday's newspapers...DAILY MIRROR Ruben Amorim has 'approved' the transfer of a player
Eddie told BBC Three Counties Radio: "I just despair with this team, a non-league team could beat us. The club should hang their heads in shame, I can never rem
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