Blades boss Chris Wilder is keen to tie down some of his stars which have helped them become unlikely Champions League contenders this term.
The Sheffield Star says negotiations are continuing to progress regarding Norwood and Lundstram who both have a desire to remain at Bramall Lane.
Lundstram is out of contract at the end of June, but fears that the club could lose him if the season restarts at a later date have been eased as his current deal has an optional 12-month extension.
Talks remain positive with the 26-year-old and his agent ,and he is expected to pen a new deal at the Blades.
Although talks with Norwood are not as advanced, the Northern Ireland midfielder still has another year to run on his contract and is eager to commit his future to the club.