Spurs were knocked out of the FA Cup on Sunday at the same time as Manchester City tightened their grip on fourth place in the Premier League with a 5-1 win over Birmingham.
Harry Redknapp's men are four points behind City heading into their White Hart Lane clash against rivals Arsenal on Wednesday, with King understood to be positive about being available following a thigh injury that has kept him out since February.
The 29-year-old centre-back has been restricted to 15 league appearances this season and will undergo his usual routine ahead of matches where a decision is made on his fitness at the last minute.
His inclusion would be a huge boost to Redknapp, who had Niko Kranjcar leave Wembley in a protective boot on his left foot after the semi-final defeat to Portsmouth.
Wilson Palacios is suspended for the Arsenal clash after picking up his 10th booking of the campaign, while Aaron Lennon has been back in training following his groin problems.
Redknapp also has Younes Kaboul and Kyle Walker available after the pair were cup-tied for the Pompey defeat.