The Jambos slipped out of Europe earlier this week with a loss at the hands of Greek outfit PAOK Salonika.
They are now focused on domestic matters and want to strengthen before the window slams shut until January.
Eyes are being drawn to an option south of the border in the shape of Tottenham midfielder White.
The 21-year-old, who is a product of Tottenham’s youth set-up, is down the pecking order at the north London club.
He had a spell on loan at Derby County in League One last term, where he made 15 appearances.
The defensively minded midfielder has entered the final year of his contract at Tottenham.
Hearts have until the closure of the Scottish transfer window at midnight to push a deal over the line, but they are facing competition from English clubs for his signature.
