Asante is back from a month-long stay with Northampton where he made four appearances, scoring once in a 2-1 away win at Morecambe.
Jervis has come back from a spell with Preston where he was on target twice in five appearances.
The 20-year-old marked his New Year's Day debut against Rochdale with a goal and also found the net in the 3-2 home win over Wycombe.
However his deal expired after the 2-1 defeat at Yeovil on Saturday and new boss Graham Westley will not be pursuing an extension having only used Jervis as a late second-half substitute in North End's past two matches.
A club statement on Preston's website read: "Preston North End would like to thank Jake for his efforts during his short stay with the club."