The 29-year-old former York City man signed a two-year deal with the Blades after leaving Millwall last month.
Asked if anything could be read into the arrival of Woolford, a player who plays in Murphy’s left-sided position, Adkins replied: “It doesn’t mean anything for Jamie Murphy.
“He is a Sheffield United player who can also play on the right and up front. As can Martyn.
“We are trying to get ourselves promoted this year and I am certainly not looking to move Jamie Murphy on.”
United are understood to remain keen on signing Billy Sharp, who has previously been linked with a possible swap deal involving Murphy joining Leeds.
Rotherham United will play a home pre-season friendly with German Bundesliga side FSV Mainz 05.
The Millers will host the Germans at AESSEAL New York Stadium on Saturday August 1 in the final pre-season friendly before the Sky Bet Championship curtain raiser against MK Dons on August 8.
Mainz finished 11th in the Bundesliga last season, and follow Premier League Leicester City as pre-season opposition.
Lewis McGugan is expected to join Sheffield Wednesday in the next 24 hours following further talks on Tuesday with his club Watford.
The 26-year-old impressed in loan spells at Hillsborough last term and would be a popular acquisition by new head coach Carlos Carvalhal.
McGugan has not travelled with the newly-promoted Hornets to their pre-season training camp in Germany and is understood to have been in South Yorkshire on Tuesday.