The ambitious Sky Bet Championship newcomers, who are in talks with potential investors in the club, are awaiting responses to their interest from Aston Villa and Southampton.
Republic of Ireland goalkeeper Given, 37, has fallen behind Brad Guzan in the pecking order at Villa Park.
Former Rovers striker Sharp, who scored 41 goals in 86 games before leaving for Southampton in 2012, spent last season on loan at Nottingham Forest.
Dickov told BBC Radio Sheffield: "Shay is somebody I know. We did make an enquiry a couple of weeks ago to take Shay on loan and we are waiting to hear back.
"Billy is somebody who is highly thought of at the club. Again, a loan enquiry did go in a couple of weeks ago and we are waiting to hear back."
However, Dickov denied rumours that he had approached Villa about another of their out-of-favour players, his former Manchester City team-mate Stephen Ireland.
"Stephen has not been mentioned, no. I think people are putting two and two together with Shay and possibly with Stephen being a friend of mine, but there has been no approach made for Stephen."