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SPFL says intention is for clubs who are unable to participate in Betfred Cup to receive a 'solidarity payment' instead.
Third-tier sides warned they could be placed in League Two for season 2021/22 if they opt to 'hibernate'.
Neilson has agreed terms and will replace Daniel Stendel at the helm.
Neilson was head coach at Hearts between 2014 and 2016.
Ibrox club added they believe some fans may be allowed in the stadium in late August.
Celtic will embark on their quest for a 10th consecutive Premiership title when the season begins.
The Pittodrie club opened talks with players and other staff last week over making wage cuts and other savings.
The midfielder and his team-mates returned to training at Lennoxtown earlier this week.
Hearts and Partick Thistle went to the Court of Session after their relegations were confirmed on Monday.
Fir Park players following social-distancing rules as they get back to business.
Neil Lennon is hopeful Celtic will have Southampton loan duo Fraser Forster and Mohamed Elyounoussi in their bid for ten-in-a-row.
Scottish Premiership club announce departures following expiry of players' contracts in May and June.
The defender has agreed a two-year deal with Jim Goodwin's side.
The new Saints boss admitted it was a difficult decision to leave Gary Rowatt and Millwall.
Aberdeen chairman Dave Cormack says he is discussions with playing and management staff.
The former Saints star returns to Perth to succeed Tommy Wright in the dugout.
The clubs are demanding either reinstatement to their leagues or compensation.
Club manager insists the integrity of Scottish women's football depends on getting City ready to play.
Revised times for Rangers' Europa League campaign and Glasgow City's Champions League ties were also announced.
Reconstruction proposals were voted down on Monday, confirming the Firhill club's relegation.