The news will be come as welcome relief to some 90,000 investors who had placed pounds 1.4bn in the once top-performing funds before trading in them was suspended for three days in early September.
Morgan Grenfell is in negotiations with Imro and Arthur Andersen, the accountancy firm hired by the regulator, to establish the basis of the compensation payments.
Devising the complex formula is set to be completed as soon as Christmas, clearing the way for the payments to investors early in the new year.
A spokesman for Morgan Grenfell said yesterday that it was too early to say what the total amount of compensation would be.
An Imro spokeswoman said the compensation exercise could not be completed until a formula had been agreed. This was an intricate task because accountants must establish the period of time over which compensation was due and the benchmark against which to measure performance.
Arthur Andersen is in the final stages of resolving issues such as whether to use the performance record of the best Morgan Grenfell fund, the best performing fund in the European sector overall or an average of the sector.
The three funds - European Growth, European Capital Growth and Europa - were among the top performers in the European sector but are now languishing at the bottom of performance league tables.
In the early days of the scandal, investors withdrew at least pounds 250m from the funds. That sum was in addition to the pounds 180m cash injection made by Deutsche Bank, the German banking giant that owns Morgan Grenfell, to buy out the highly unusual investments made by Peter Young, the former fund manager.
Mr Young had set up a web of shell companies to buy up large stakes in high technology firms across Europe and America. He is currently under investigation by the Serious Fraud Office, which is working to establish if he benefited personally from the investments.
His assets have been frozen and his passport confiscated but he has not been charged with any offence.
He started managing European Growth and European Capital Growth in 1994. While the funds were only suspended in September, evidence of unusual activity has been established dating back to the summer of 1995.
Evidence such as this will be used to help determine the time frame over which compensation will be due.
Deutsche Bank, which has deep pockets and has pledged to compensate investors, does not yet know the size of the compensation bill, which some reports estimate at pounds 200m.
Penalties are also expected to be levied by Imro. Morgan Grenfell is braced for a fine of at least pounds 1m, Imro's largest ever, early in the new year.