Gascoigne has been without a club since a brief spell playing in China. He trained with Wolves after returning to England, but has yet to prove his fitness.
Evans said: "I've not lost any enthusiasm in getting him down here, so hopefully the situation will become clearer when we hold further talks early this week."
The Pilgrims have additional funds to attract Gascoigne to the club, after £2,000 a week striker Derek Lilley had his contract cancelled weeks after signing.
The Scottish striker has returned to Scottish Premier League side Livingston after his wife failed to settle in Lincolnshire.
*Boston have also unveiled plans for a new £7.5million stadium, which they hope to share with neighbours Boston Town.
It will have a 7,500 capacity as well as a car park, function rooms, computer learning centre and a 90-bedroom hotel.