Well on the Democrat side Gallup did a series of polls in 1939 and 1940 asking Democrats who they wanted as their candidate if FDR did not run for a third term.
As of the June 1940 poll (the last poll in the series), Cordell Hull was in the lead with 47% of the vote. (His next closest competitor was John Garner with 23%).
Hull's support had also increased dramatically over the course of 1940. In the December 1939 poll he was only at 8% (compared to Garner's 58% and McNutt's 17%), and in the February 1940 poll, Hull was still trailing Garner with 25% of the vote to Garner's 40%. I assume the dramatic rise in support for Hull was due to Democratic voters wanting a candidate with foreign policy experience given the deteriorating international situation.
http://ibiblio.org/pha/Gallup/Gallup 1940.htm
Thus I think the Democratic presidential candidate would most likely be Cordell Hull (who FDR would certainly prefer to Garner). As for his veep, since Hull is from the south, he would probably need a northern to give the ticket geographic balance and as such James Farley would make a lot of sense.
On the Republican side, it probably depends on events in Europe. If World War 2 has been avoided or is going significantly better for the Allies than IOTL then the candidate is probably Thomas Dewey who IOTL dominated the early Republican primaries and ran the strongest against Hull in a Gallup poll. (The May 1940 poll of a Hull-Dewey matchup had Hull at 51% and Dewey at 49%). However, if events in Europe play out similarly to OTL (with France falling right as the GOP convention begins) then I imagine there would be the same reluctance to nominate "a 38 year old kid whose foreign experience was limited to a bicycle tour of France fifteen years before" that derailed Dewey's OTL run, and so Wilkie probably still gets the nomination. (Taft and Vandenberg being unacceptable alternatives due to their isolationism.)
Regardless of whether the GOP presidential candidate is Dewey or Wilkie, Charles McNary still makes a lot of sense for their veep since both Dewey and Wilkie are Washington outsiders and weak on farm issues, and thus McNary, a senator with nearly 30 years experience, who is an expert on farm policy, will fill in a lot of gaps in their resumes.