The bill, announced by Theresa May at the Conservative conference in October, will scrap the European Communities Act and move EU laws on to the UK statute books.
The new law would end the EU’s legal supremacy in the UK and concerns have been raised it could put workers’ rights and environmental standards under threat, which UK Brexit minister David Davis has denied.
Giving evidence at the Scottish Parliament’s Finance and Constitution Committee, Mr Russell said: “It is the view of the Scottish Parliament that we should take a view on the Article 50 process and that the Scottish Parliament should have a consent motion.
“That is up to the triggering of Article 50. Beyond that, I think it would be a reactive process to see what the parliamentary process is. For example, the Great Repeal Bill is for the next parliamentary session at Westminster, there are considerable issues in that for Scotland.
“Will that require a separate Scottish bill? It should require a legislative consent motion if it doesn’t have a Scottish bill. All those things will have to come forward.”
He also called on the UK Government to offer “reassurance” to people and provide detail on its negotiations to leave the EU, instead of offering “private reassurance” such as the letter to Nissan on car manufacturing. The letter helped persuade the firm to stay in the UK.
Mr Russell added: “I would hope that they would be transparent, not in terms of the everyday of negotiation.
“I accept that you don’t negotiate in the full spotlight but you do have to be open about the principles you have and you do have to offer reassurance to people, and that reassurance must at least in part be public.
“The Nissan letter is an example of private reassurance which raises alarm bells, which makes other people wonder if they have been excluded rather than included.”