The Gunners have seen two bids rejected by the Reds so far in the current transfer window, but the Uruguayan is said to be keen on a move to the Emirates Stadium.
However, Rodgers believes that Arsenal have taken too long in their negotiations and have missed the period in which Liverpool would have considered allowing Suarez to leave.
"There is always a timeline where you would never sell and we are at that stage now because we're so close to the beginning of the season," Rodgers told reporters. "We are focused on Luis being here, getting in a couple more and ready to be challenging at the top of the table.
"As time goes on I am gaining more confidence that he will stay and the owners have been brilliant. Maybe if it was another club where they needed the money it could be a different story.
"They have been first class through the whole process and that fills me with confidence that they are in no hurry to sell. They understand that they are trying to build. There has been lots of talk but the board have been very strong."
Suarez joined Liverpool from Ajax in January 2011.