On Wednesday, Hughes confirmed that the Premier League side had bid for the 25 million-euro rated Cameroon international but the forward remained undecided over his future after being offered a new two-year contract by Barcelona.
The City manager said he would exercise as much patience as needed to take Eto'o to Eastlands but confirmed he would walk away if the situation dragged on and he felt he could not take it forward.
"We've lodged a bid for Samuel Eto'o, that's already been reported," Hughes told reporters.
"We have targeted players we think can help us and he's certainly someone we have a lot of respect for and we feel he can help us.
"There's always an element of frustration when you can't conclude deals very quickly, but we'll give every deal the patience it deserves.
"If we get to a situation where we feel that things aren't going to happen and we feel the process is stalling and we can't move it forward then that's the time we walk away.
"We've done that before.
"We obviously made an offer to Barcelona and now there seems to be a situation between the player and his club.
"We're not involved in that. That needs to be resolved between the player and his club.
"Patience has been mentioned and we'll all have to be patient."
Hughes also confirmed he was still hoping to sign Carlos Tevez after the Argentina striker's loan expired at neighbours Manchester United.
"Carlos Tevez is another player I have huge admiration for," Hughes added.
"We'll see what happens but at this stage it's very early in our discussions with anybody."
