Manchester City and Everton are also keeping tabs on Brown, whose contract runs out at the end of the season.
The Yorkshire Post says personal terms are no longer the stumbling block but issues relating to future contract negotiations need to be resolved.
Paddy Kenny and Michael Tongue have just tied themselves to long-term contracts at Bramall Lane and Blades boss Neil Warnock hopes Brown will follow suit.
Warnock said: "Michael knows we want him to stay and I don't see any reason why he cannot maintain his high standards over the next three or four years.
"I will be speaking to him after the Reading game (tonight) because we finally have a blank week. The contract situation is in his hands, we have made him an offer and he is thinking about it."