The 35-year-old took over from Michael Laudrup in February but the Swans have gone six Premier League games without a win and are just five points above the bottom three
A central defender at the club for 10 years, Monk took over in February following the departure of Michael Laudrup and guided the Swans to a 3-0 win over fierce rivals Cardiff City in his first game in charge.
Since then, however, the Welsh club have gone six league games without a win and sit 15th in the table, five points clear of the bottom three.
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"Probably," he told the press. "I'm not stupid.
"I'm not thinking about my own position, I'm just trying to do what I can for the club."
Monk says that he has to plan for life in the Premier League next year but that he has not yet discussed potential transfer targets with chairman Huw Jenkins.
"Hopefully we're safe as soon as possible and we can have that conversation but we're not in that position right now," he added.
"I don't want to get to a position where I haven't prepared for next season but, in terms of transfer targets, no, I haven't had that conversation with the chairman.
"I've put this club ahead of me for 10 years so I'll do that until I'm asked not to."