Swansea, in 14th place, travel to take on Liverpool on Sunday and Monk said the Welsh club believe he is the right man for the job.
"I speak to the chairman and he is extraordinary supportive. That word trust is from top to bottom, from him, when I have my discussion with him. It is normal," Monk told reporters on Friday.
"It is normal to have discussions with chairman and the board. Talk about performances, football in general, what went well, what didn't go well, what has to be improved and how we go about that as a group.
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"All those things, that world trust is something that is clear from him.
"He trusts how I work, he's seen the success, what I bring to the club has worked in the past and he knows we can get through this period if we are all united, which we are, and we make sure we get through it and come back to our best," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru)
