Johnson is due to announce a shake up to his Elite Performance Squad on Wednesday and Jones was speaking in the wake of another match winning performance from his Kiwi-born outside half against Bristol this weekend.
Now 33, Jackson joined the Sarries in 2004 and has since become their all-time record points scorer and become England qualified. He played for the Waikato Chiefs in the Super 12, Bay of Plenty in the NPC and was in the New Zealand Maoris squad before joining the Guinness Premiership outfit.
"England should really consider having him in the squad. His goalkicking is good and his out-of-hand kicking is just wonderful," said Jones after seeing Jackson pick up 15 points in a 37-13 demolition of Bristol.
"If England are going to have Danny Cipriani and Toby Flood as their major stand-offs, maybe they should have someone like Jackson, who understands the game exceedingly well, in the squad to teach these younger guys how to play. I think they need a mentor."
England have already blooded New Zealand immigrants Mark van Gisbergen and Rikki Flutey in recent seasons and Jackson could follow suit. If Johnson did pick him, then he could also come into the reckoning for a British & Irish Lions tour place this summer.