The defending Scottish champions agreed a pre-contract with the 25-year-old earlier in the January transfer window.
However, Rangers are unwilling to wait until the summer to secure the Scottish international and have tabled a bid to immediately sign him before the transfer window closes.
However, Hearts have rejected that fresh bid, according to Sky Sports Scotland.
With time running out it remains to be seen whether the Glasgow giants return with a fresh bid or wait for a few months to eventually get the player among their ranks.
Souttar had earlier rejected an offer from Hearts to extend his contract as he preferred to take up a new challenge.
He had interest from English Championship as well but decided to stay put in Scotland to sign for Rangers.
He has represented Scotland four times since his debut in 2018.
Rangers have been active in the transfer market on deadline day securing the services of Mateusz Zukowski from Polish outfit Lechia Gdansk and have also been linked with a move for Aaron Ramsey.
