Shongwe, who still has one year left on his Bidvest Wits contract, is not part of Gavin Hunt's plans for this season.
Wits have made the player available and he was previously linked with a move to Kazier Chiefs and Orlando Pirates but nothing materialised.
Arrows have now signalled their interest and coach Clinton Larsen says Shongwe is a player he would love to have.
"Our club is talking to him and I have got no idea [what progress has been made] but all I know is the two clubs are talking," Larsen tells KickOff.com.
"I know the club was given permission for him to be here. The agreement between the clubs is between the two bosses.
"He has started training today and it is why we have invited him because we rate him quite highly. I think everybody knows Jabulani and the quality he's got, so we are hoping we can finalise something with him."