Everton earned a 2-0 win over Swansea City's second string.
Henen's existing Everton deal expires at the end of the campaign.
Baxter returned to Everton last year, 12 months after his release by Sheffield United.
Everton defender Ramiro Funes-Mori played for the Toffees' development side and impressed.
Everton Under-23 manager David Unsworth has been linked with Oxford United, Barnsley and Bradford City.
The Everton Under-23s coach could still be on the move despite rejecting Oxford United this week.
Everton coach reportedly wants to stay put.
The Everton under-21 coach has rejected the chance to take over at Oxford United.
The players from the Everton Under-23s that David Unsworth currently manages that he could target if given the Oxford job.
The prospective Oxford appointment stepped in as Everton caretaker boss earlier this season.