Albion boss Carlos Corberan is keen to bolster his midfield options having lost Matty Phillips to recovery from surgery possibly until the end of the season.
The Spaniard has dragged the Baggies from being in a relegation battle to chasing promotion via the play-offs since replacing Steve Bruce at The Hawthorns - but their momentum has been stalled by a league defeat to Burnley and an FA Cup exit at the hands of Bristol City.
The weekend defeat to City has galvanised Corberan as he was not impressed with the performance of some of his fringe squad players, who put in a limp display at Ashton Gate.
Aston Villa midfielder Marvelous Nakamba was on Albion's radar as it seemed a deal for Chalobah was not viable - but the Fulham man is believed to be having a medical at The Hawthorns ahead of a permanent move to the Baggies.
Chalobah, 28 and 6ft 2ins, will add some physicality to the Albion midfield and has made 12 league appearances for the Cottagers since joining for £3million from Watford in August 2021.
He is unlikely to be the only deadline-day addition to West Brom's squad, though, as Albion are also chasing the signature of 21-year-old Spurs midfielder White.
The Londoners are happy to send White out on loan for the rest of the campaign and Corberan's play-off chasers are one of a number of Championship clubs interested, according to reports on the Express & Star.
Albion had also been in the running for Nottingham Forest midfielder Lewis O'Brien, who worked with Corberan when the duo were at Huddersfield Town.
But a £10m obligation to buy clause in the loan deal has put the Baggies off - and left Sheffield United and Blackburn Rovers in the hunt for his signature on Tuesday.
READ MORE: West Brom target Aston Villa flop Marvelous Nakamba but miss out on Forest's Lewis O'Brien