I am aware that there are a number of early church fathers who made this connection (e.g. here and summarized here). Is there also material internal to Mark's gospel to suggest that it reflects the memoirs of Peter?
There is no conclusive internal evidence but there are plenty of pointers that lend themselves to the conclusion that Peter is in some way the source, for example this list from here:
Of these I give the last the most weight.
Also, only Peter, James and John were present at the transfiguration, so it is likely that one of them passed on the account to Mark:
This is very similar to Peter's account in 2 Peter:
So, Is there also material internal to Mark's gospel to suggest that it reflects the memoirs of Peter?
Yes, but the key word here is "suggest". There is no direct proof but also no strong reason to suggest otherwise, which is important too.
Here is the various internal evidence that I am aware of, as well as evidence that indicates a "persecuted audience" which fits the idea of this being written after Peter's death at the hands of Nero.
Evidence That could Indicate Peter as an Original Source
Internal evidence indicating a setting of persecution: