Tom Penn and Amin Elhassan explain what they think the Boston Celtics should do with the third pick of the 2016 NBA Draft. (2:04)

The Boston Celtics have been pursuing a number of established veterans in the buildup to Thursday's NBA draft, offering trade packages built around the No. 3 overall pick, according to league sources.

But sources told ESPN that the Celtics, to date, have been rebuffed in their efforts to assemble a sufficiently enticing deal to acquire any of these four prime targets: Chicago Bulls All-Star swingman Jimmy Butler, Utah Jazz guard Gordon Hayward and Milwaukee Bucks teammates Jabari Parker or Khris Middleton.

Who the Celtics like at No. 3, if they end up keeping the pick, has likewise emerged as one of the bigger mysteries of draft week, sources say.

The Bulls, sources say, continue to show little interest in dealing Butler to the Celtics, who previously tried to trade for him before the league's annual deadline in February.

Sources say the Celtics are one of just a number of teams trying to convince Utah to surrender Hayward -- Phoenix, which holds two lottery picks (No. 4 and 13) in Thursday's draft, is another -- but the Jazz have been telling interested teams that he is not available.

The Celtics continue to show interest in the Bulls' Jimmy Butler after also trying to trade for him before the deadline in February, sources say. Joe Murphy/NBAE/Getty Images

The same, sources say, goes for Parker and Middleton in Milwaukee, since the Bucks regard both of those young cornerstones, as well as Giannis Antetokounmpo, as untouchables.

The Philadelphia 76ers, sources say, have been trying for some time to convince the Celtics to part with the No. 3 pick in a deal headlined by Sixers big man Jahlil Okafor or teammate Nerlens Noel, but Boston, to date, has resisted those pitches.‎