Hadden said he would monitor Danielli's progress and he announced: "Simon has returned from holiday and been assessed by our medical team.
"His injury was not as bad as first feared and we have decided that he is worthy of consideration for a place in our Rugby World Cup squad.
"Competition for places in our back three is already fierce and it intensifies with Simon's inclusion."
Danielli said: "I'm delighted to be back and intend to battle hard over the next few weeks to prove my fitness and try to win a place in the final Rugby World Cup squad."
Danielli's call-up takes the number of players involved in the two-phase preparation to 39.
Players are currently working on a strength and conditioning programme under the guidance of Scotland fitness coach Mark Bitcon.
In July, the focus will move on to rugby preparation ahead of the Bank of Scotland Corporate August Tests against Ireland (August 11) and South Africa (August 25) both at Murrayfield.