Ashton is out of contract at Franklin's Gardens this summer and has been in talks with the Aviva Premiership champions, which are said to be progressing well.
The 24-year-old is understood to want his future tied up before England launch the defence of their Six Nations title.
Venter told EWN Sport in South Africa: "The nice thing with Chris is he is a very talented individual which any team would love to have.
"I think there is a process in having a discussion with him and there must probably be an announcement in the next couple of weeks."
Ashton has scored 15 tries in 18 Tests for England and 95 in 105 appearances for Northampton since his cross-code switch from Wigan in 2007.
Northampton have already made clear they will not break the bank to keep Ashton.
Saracens have spent the last week in Cape Town preparing for their Heineken Cup clash with Biarritz, which the club had initially wanted to play in South Africa.
Local issues over which Cape Town stadium would host the game forced Saracens to bring the vital fixture back to Vicarage Road.
Venter denied the squad's temporary relocation this week, and the travel involved. would have any detrimental affect on the squad.
"It's lovely travelling to South Africa and the people are unbelievably friendly," he said.
"Everyone has had a good time but one thing this team prides itself on is switching on and off for the big games. I think we will play well."
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