The newspaper claims that the Middlesborough recruitment team thought there was a chance to land the 30-year-old as the Hammers are reportedly interested in signing England international Joe Hart this summer.
This follows up from the story in the Evening Standard which reported that West Ham boss Slaven Bilic is looking to complete a deal for the Manchester City keeper in the next few days.
The Northern Echo reports that the Premier League side are not interested in selling the goalkeeper even if they secure Hart’s signature this summer as they plan to keep Randolph as their back-up option ahead of current shot-stopper Adrian.
The Championship side might already have a replacement in mind as the Chronicle recently reported that Middlesborough are in ongoing talks with neighbours Newcastle United to sign goalkeeper Karl Darlow.
Randolph enjoyed his best campaign with West Ham in terms of games played last season as he made a total of 27 appearances in all competitions.
The Republic of Ireland international produced some impressive performances and he managed to keep a total of six clean sheets in the process.
The goalkeeper has spent two years in East London but he only managed to establish himself as the number one last season following Adrian’s dip in form.
Randolph’s current contract at the London Stadium runs out in 2020.