You don't need to enter the payer's TIN if it isn't shown on your mutual fund statement. You can use your year-end statement to report your earnings. However, it's best practice to wait until you receive your 1099 to help ensure your records match the records sent to the IRS by the payer. You can check the payer's website and contact them if needed.
For more detailed information, you can refer to:
IRS guidelines on reporting investment income
Turbo Tax Guide - No 1099