Manager Robbie Neilson reported that, as far as he is concerned, Ginnelly is out for the rest of the season after surgery on a ruptured hamstring.
Talks between Hearts and their on-loan Preston North End winger about a permanent contract for next season began last month before injury struck.
White, the versatile left-back often deployed in a left-wing role by Neilson, trained this week after missing the last two matches with his own hamstring complaint.
He will be in the squad which travels to face Inverness Caledonian Thistle. The Highlanders are under new management with Neil McCann standing in while John Robertson is on compassionate leave.
“The boys are fine. Everyone is back in other than John Souttar and Ginnelly. Aidy White is back training with us and he will be available,” confirmed Neilson.
On Ginnelly possibly returning before the season finishes, he added: “It’s not a subject we have broached. After he had his operation that was him done for the season and there has been no change as far as I am aware.”
The Hearts community have offered enormous support to Robertson since he was given leave of absence on Monday following a family bereavement. He is the Edinburgh club’s record league goalscorer and very much a living legend in Gorgie.
“I haven't spoken to him yet,” admitted Neilson. “I dropped him a wee Whatsapp message the other day to say we are all thinking about him. It's a very difficult period for John and his family.
“I've known him for a long time and hopefully we see him back on the touchline as soon as he's ready. We all have families, we all have background problems, so it’s a huge credit – first and foremost to John – for taking that decision to step out for a little bit to look after his family.
“Secondly, from the club’s perspective, it good to stand by him and give him that support. I know Kell [Stuart Kellacher] his assistant is off with an issue as well just now.
“So it has been a really tough period for them. Credit to the board up there and [chief executive] Scot Gardiner that they’ve allowed John to do this.”
McCann returns to a technical area for the first time since being sacked by Dundee in October 2018. He and Neilson were Hearts team-mates between 2006 and 2008 and the so-called ‘new-manager bounce’ is something Neilson is wary of.
“Obviously there will be the wee lift of someone coming in to stand in for John,” he said. “There's a quick turnaround of games for Inverness – they played on Saturday, then on Tuesday night, then again on Friday – so there's not a lot of time there to work on formations and how the team will play.
Opportunity for McCann
“I expect them to play much the same way as they have for the majority of the season.
“I think Neil will see it as an opportunity to firstly help John out. He'll know him from his time at Hearts in the mid-to-late-90s. He will obviously want to help the club out as well with Scot Gardiner there.
“It's a good opportunity for him to get back on the touchline. I know he enjoys being there and wants to get back into it as well.
“It's difficult to get back in and difficult to get back into the right job. I'm sure he's had a number of opportunities but maybe just not the right ones for him.
“He's obviously been doing a lot of TV work as well. You have to balance that off: Is it worthwhile going back in if it's not the right job? Or do you wait for the one you feel will be the most beneficial for you and the club?
Inverness have already set a new attendance record for Friday’s fixture, although the Caledonian Stadium will remain empty for the BBC Scotland cameras.
Virtual ticket sales are pushing towards the 10,000 mark thanks partly to the generosity of Hearts supporters.
“I thought it was brilliant,” said Neilson. “Firstly, it was a great idea to go and do it. The link between the clubs goes back a number of years to when Hearts were in trouble back in 2013.
Strength of fans
“So it’s great to able to reciprocate that with money going back to Inverness to help them at this difficult time. It shows the strength of the Hearts fans, and fans in general.
“There have been a lot of fans from outwith ourselves and Inverness who have bought tickets to try and help them out. We’re pleased to see it, but I’m not surprised to be honest with you.
“Breaking an attendance record through a virtual attendance is a great thing to do. Hopefully we can put a good performance and get the three points and thank our fans for coming out and supporting Inverness.”
Hearts’ need for victory in the Highlands intensified after draws in their last two fixtures – away to Queen of the South and at home against Morton. The Championship leaders still have an 11-point lead but know they must be more ruthless.
“It’s just about remaining calm and doing the things we’re doing. We’re going to have games every so often where we create chances and it doesn’t quite happen for you on the day,” explained Neilson.
“We’ve had other games this season where we have had far less attempts at goal and scored more goals. So we have had a chat about concentrating a little bit more when we get those opportunities and make sure we take them.”