You could try something along these lines:
Dim intReports As Integer, rpt As Report
Dim ReportName As String
intReports = Reports.Count
If intReports = 0 Then
Exit Sub
Else:
For Each rpt In Reports
ReportName = rpt.Name
If ReportName = "Your Report Name" Then
MsgBox "This report is already open"
End If
Next rpt
End If
I use a modified version of this to determine if a report is open and if so to leave a form open or close it or whatever is required. I find it quite effective.
You could probably also set up some sort of variable and an additional looping structure if you wanted to check against all your report names, depending on how many you have.
Hope this helps. email me if any of this needs further clarification.
