Pools boss Colin Cooper hoped to see the experienced midfielder appear against Bradford at the weekend, but instead Greening turned out for Blackpool in their friendly with Burnley.
The Tangerines have been in turmoil this summer and, until two weeks ago, only had eight players signed up.
On Saturday, they listed seven un-named trialists as substitutes, but Greening was among them and Cooper admitted Pools couldn’t compete financially with what the Championship club could offer.
Pools drew 1-1 with the Bantams and Tommy Miller played his fourth game since returning to the club on trial, with Cooper ready to make a decision on the future of the midfielder.
Cooper has so far only signed Matthew Bates and Stuart Parnaby and fully expects to add to his ranks this week ahead of the opener at Stevenage on Saturday.
“I’ve been fairly relaxed about everything,’’ he insisted.
“Players are now wanting to commit and clubs are now wanting to send players out on loan.
Teams we are talking to know what we are looking for. Things are starting to fall into place.’’ Pools’ goal came from Bradley Walker, but it was soon cancelled out by Billy Clarke. Centre-half Sam Collins was forced out of the game when he was felled by a shot by former Pools’ team-mate Gary Liddle.
A young Pools team goes to Spennymoor tonight and Cooper said: “Bits and pieces were good. I felt we needed more intensity about the way we did things and I felt we got that.
“We looked a bit more lively. There’s more we can do, but at least I feel we are heading in the right direction rather than a negative, passive direction.
“While not perfect, at least we showed signs we are taking on board what we are talking about and it gives us confidence going into Stevenage.’’