The left-back was the subject of frequent bids by the Premier League champions over the summer but, even while Marouane Fellaini was sold to Old Trafford, the Toffees held firm
The Red Devils bid repeatedly for both the left-back and midfielder Marouane Fellaini throughout the summer but eventually had to settle for only the Belgian, agreeing a £27.5 million deal late on transfer deadline day.
Speaking at a Football Writers Association event, Stubbs confirmed that the Toffees drew the line at selling Baines before recruiting the likes of Romelu Lukaku, Gareth Barry and James McCarthy late on.
"The way the transfer deadline goes, everyone looks at it and it got to a stage where we knew the Gareth Bale [to Real Madrid] thing was going to happen," he recalled. "That was the big one. Underlying from that, there wasn't really an awful lot going on.
"Probably come seven o'clock on the night [September 2] at Everton the word from the training ground was that no one was going to go.
"Fellaini was staying. Bainesy was never really an option - the club had dug its heels in. Bainesy had obviously said he'd like to go.
"And then, come nine o'clock, suddenly we started to get linked with Lukaku and then the Fellaini thing was starting with negotiations with United. By the time it had finished we'd bought three in and they are great additions to the squad."