Britton was restricted to only seven Premier League starts this season and has been told by Monk his chances of regular first-team football are unlikely to improve ahead of next term.
The 32-year-old is yet to speak to any other club and insists he is in the dark over reports he could move to the MLS, but he is open to the idea of leaving the Liberty Stadium this summer.
“I spoke to the manager just before the end of the season and we talked about the frustrating season I’d had,” Britton told the Swansea Evening Post.
“I started off with an injury, then I picked up a few niggles and some illness which meant I had to pull out of games which I was supposed to play in.
“Jack Cork has come into the club and he has done brilliantly and the team have done brilliantly, so I can’t complain.
“I am not complaining – there are other players who haven’t played as much as they would have wanted and you are always going to get frustrated when you are in that position.
“When I spoke to the manager, he said that he sees things being very much the same next season, if not (worse) with me being out of the squad completely because he is trying to push young lads like Jay (Fulton) and Matt (Grimes) through.
“They are the future of the club, I understand that.
“But if they take my place in the squad, I am going to be training all week and then running round the training ground on my own on a Saturday, and that’s not what I want at my age.
“I said to the manager that I can’t do another season not playing.
“I have two years left on my contract, but I am 32 and I don’t want to be not playing at this age, so I have said to the manager that I will look at my options.”
Despite preparing to look elsewhere, Britton is not ruling out remaining in south Wales should a door back into the first team unexpectedly open.
“You never know what can happen, someone could get injured and there could be a chance for me to get back into the team,” Britton added.
“But I have to look at things the way they are now, and as it stands the manager feels it will be difficult for me to play.
“I am not someone who will be happy to play every couple of months or whatever and then pick up my money.
“My first choice will always to be play for Swansea – I would love to finish my career at the club.
“But I still feel I have got something to give and I am not going to be happy not playing.
“I want to play here, but if the chances of that happening are limited I will have to look at what options are out there and I have spoken to the manager about that.
“I don’t know whether it might be a loan or a permanent move and I don’t know where it could be to, whether it’s another Premier League club, a Championship club or abroad somewhere.
“I haven’t really been in this position before – not since I went to Sheffield United – so I will just see what options are out there.
“If there are any, I will talk to the manager and the chairman and we will see what everyone thinks.”