The Gers are in the market to bolster their defence and should look to sign the experienced Everton centre-back who is available for free.
The 40-cap England international is without a club at the moment after his contract at Everton expired.
Jagielka has been with Everton since 2007, emerging as their Player of the Season in 2008-09 and in 2014-15.
He is a vastly experienced Premier League player and Steven Gerrard knows about his quality very well, having played with him for England.
According to reports from the Scottish Sun, Scottish Premiership champions Celtic are looking to sign Jagielka this summer.