The Fratton Park outfit had already accepted a £17.5 million bid from Liverpool this week, with the 24-year-old set to link up with Rafael Benitez at Anfield.
However, Carlo Ancelotti's Blues have now entered the race for the former West Ham full-back.
Chelsea bought Johnson from the Hammers for £6 million in 2003, before selling him on to Pompey for around £4 million four years later with the defender having made 41 league appearances for the Stamford Bridge club.
"The matter will come to a conclusion at the beginning of next week. I do not have a preference over the move, it is up to Glen," said Portsmouth chief Peter Storrie.
"The deals are almost identical so it really is down to him and what club he prefers, which one is going to pay him more money.
"Glen wants to play regularly in the Champions League, he has got himself back in the England side so I understand that. Sometimes you have to be fair to players.
"It's a big year for him with the World Cup coming up.
"Playing Champions League football will make him an even better player than he is today."
Johnson has made 84 league outings for Portsmouth after originally arriving on loan in 2006, netting four times including the spectacular long-range volley at home to Hull City in 2008/09 that was named goal of the season.
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