The 35-year-old midfielder looked to be on his way out at the Keepmoat Stadium but a deal failed to materialise before the transfer window closed on Tuesday.
Wellens wanted to move back to his native Lancashire to be closer to his family home.
The former Manchester United and Leicester City midfielder will not be considered by Dickov for this weekend’s League One trip to Gillingham.
And Wellens looks set to leave Rovers next week when the loan window re-opens, having been linked with Wigan Athletic.
Dickov insists discussions have been amicable between the club and player, and still hopes Wellens could stay if a loan move falls through.
“You never say never in football,” said Dickov. “If a move doesn’t materialise, Richie will come back and be 100 per cent committed.
“The move has to be right for us. Right for Richie, location-wise, but right for me and the club.
There’s no guarantee it’s going to happen.
“Richie is a top player and I will be sad to see him leave. I completely understand his reasons - which I will keep private - and we move on.”