Wolves made a £3million offer to sign the English midfielder before the summer transfer window closed last week, but that bid was deemed well below Fulham’s asking price and promptly rejected.
Reed, 28, was open to the move to Molineux but would also be keen to stay at Craven Cottage should he be presented with suitably improved terms.
The £6million signing from Southampton - who also has interest from Everton - remains on the same £30,000-a-week contract he signed after joining permanently in summer 2020 following a productive loan spell in west London.
That deal expires in 2024, albeit with Fulham possessing the option to extend it automatically by a further year.
Reed has made a total of 150 appearances for the Cottagers across all competitions so far, scoring three goals and laying on 11 assists.
He has appeared in all five of Fulham’s matches so far this term, starting four and coming on as a substitute in the west London derby against Brentford.