The defender has signed a contract extension at Bramall Lane keeping him at the Premier League club until 2022.
Basham had been linked with a move to Newcastle, the club which released him when he was 16. However, the Gazette understands that the 32-year-old was not among the club’s primary summer transfer targets,
Speaking about his extension, the boyhood Sunderland fan said: "When the transfer window starts to open, there's always a bit of talk. There's always going to be that paper talk, but it wasn't (a possibility for me to leave). The manager (Chris Wilder) pushed as much as he could, and we all said after lockdown 'let's get it done'.
Newcastle United to ‘push ahead’ with £48m double raid, Toon in ‘pole position’ for £42m Tottenham star
Tottenham Hotspur star ‘banished’ from squad amid Newcastle United speculation - reports
Newcastle United ‘in talks’ over Chelsea duo, Toon set to walk away from ‘£60m’ discussions
Newcastle United 'closing in' on £13m striker following St James's Park visit
What Eddie Howe has said on Newcastle United transfers as club prepare €30m Goncalo Ramos bid
"I was desperate for it to happen, to be honest, and it probably played on my mind a bit too much at times. I'm buzzing to have it signed.”