Welsh, 23, came through the youth ranks of the Bhoys but has yet to establish himself in the backline at Parkhead.
The defender attracted interest from across Europe last year and Celtic snubbed loan-to-buy offers for Welsh from Udinese and Toulouse during that period.
This year he is also said to be subject to transfer interest from Bundesliga and Serie A clubs in the ongoing transfer window, though the Scottish Premiership title holders have yet to decide on his future.
Now it is mooted that any decision on Welsh will be taken only after Rodgers has gauged the Hoops squad, with the player still having two years left on his contract with the Scottish giants.
However, Rodgers’ side are already off and running in the transfer market and have snapped up two targets in the shapes of Odin Thiago Holm and Marco Tilio.
The Scottish centre-back featured only four times during Celtic’s title-winning campaign last season but it is still unclear whether he is keen on leaving Parkhead this summer.
Now all eyes will be on Celtic to see whether they hold on to Welsh this summer or open the Parkhead exit door for the centre-back.
