The Owls have been 'heavily linked' with James Beattie and Ryan Needs, both of whom have previously worked with the Hillsborough manager.
The 40-year-old was appointed to the Owls hotseat on 6 September, replacing Steve Bruce who resigned a few months prior, and has overseen three wins, one draw and two defeats from his first six games in charge in all competitions.
Monk has yet to add to his coaching team, but according to The Star, Wednesday have been "heavily linked" with Beattie and Needs, both of whom have worked with the Owls boss at previous clubs Swansea, Leeds, Middlesbrough and Birmingham.
"If I get the opportunity to bring in some staff that I think are needed in certain areas to strengthen us, then of course I will do that," Monk told the outlet. "But, at this moment in time, it is what it is. I am just concentrating on the staff and the players that we have here right now and that is all we can do."
Following Monk's arrival, caretaker manager Lee Bullen stayed on to assist the new boss along with coach Neil Thompson and goalkeeping coach Nicky Weaver, and the Owls manager paid tribute to his current setup.
"The staff here have been fantastic," he added. "They have been really supportive. It is not easy for them to take on my ideas and methods but we have all worked really hard; harder than the players. We spend a lot more hours at the training ground going through certain things. Bully, Thommo, Nicky and the rest of the guys have been fantastic."
Following the international break, Wednesday return to action on Friday 18 October with a trip to Cardiff City.
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