HITC Sport understands that the League Two outfit are hoping to have the midfielder with them next week.
The 21-year-old midfielder is currently with Dulwich Hamlet but is only on non-contract terms, so any club could sign him under the seven day approach rule, which is commonly used in non-league football.
Sweeney, who only joined Dulwich from Kingstonian this season, has created a real buzz during his dozen or so games - and a number of League clubs have been trailing him.
Reading were keen and he spent time on trial with the Royals last month, as revealed by HITC Sport, before he returned to Dulwich - but now Hartlepool have made their move and hope to be able to have Sweeney in the North East next week.
Pools are looking for recruits that can help to lift them away from the wrong end of the League Two table.
Having battled to beat the drop last season, they are currently eight points above the drop zone and have lost four of their last five fixtures.