Monk, 35 and still registered as a player for the club, took over on a temporary basis when Michael Laudrup was sacked in February.
The defender has never hidden his desire to continue a 10-year spell at the Liberty Stadium as full-time boss, but Swansea are not yet safe, lingering six points above the drop zone.
Ahead of a huge relegation clash with Aston Villa on Saturday, Monk told Sky Sports News: "I'm sure in the near future that talks will be happening.
"Hopefully I will sit down with the chairman and the board and see where they want to go and what part of their plans I come into.
"But my future is not down to me. I'm just focused on what I'm doing right now, trying to get the win against Villa."
The south Wales club grabbed a crucial victory away to Newcastle last weekend but they have failed to win successive league games all season.
"Consistency-wise we haven't been there. It's been a problem all campaign. We have a chance this week to right those wrongs and try to win back-to-back games," Monk said.
"We just want to finish with 40 points, it's a minimum target for us. We need to set a standard and that's what we're aiming for."