Although not a very perfect solution, I did something like this. I created a .sh file and added this codes.
#!/bin/bash
Output File
output_file="nohup_output"
nohup command > "$output_file" 2>&1 &
while true
do
if tail -n 1 "$output_file" | grep -qF "$current_datetime"; then
sleep 1
else
tail -n 0 -f "$output_file" | while read -r line; do
current_datetime=$(date +"[%Y-%m-%d %H:%M:%S]")
echo "$current_datetime $line"
truncate -s 0 nohup_output # To delete inside the nohup_output file
done >> "$output_file.log"
fi
done
In this way, I got printouts containing the date and time as I wanted.